Digit substitutions by ‘+’ and ‘=’ signs

(inside an integer)

 

 

[January 26th, 2009]

 

Hello Math-fun,

 

... stupid idea, yesterday, to get asleep:

 

Let's examine a 5-digit integer like abcde; if we decide that b is the + sign and d the = sign, we have the simple equation a+c=e.

 

This equation has a lot of solutions (like 1+2=3 or 1+0=1)... but once we have decided that (for instance) 4 is coding "+" and 8 is coding "=", we cannot use elsewhere (in the integer) the digits 4 and 8.

 

Thus, with the [4+;8=] convention, a valid 5-digit integer would be, for instance, 14283. Or 14081. Or 18041 (1=0+1). But not 24284 (2+2=+). Neither 04585 (no leading zero).

 

Questions:

 

a) What is the best [x+;y=] coding in order to produce the biggest quantity of valid 5-digit integers?

 

b) Same question for a 6-digit integer?

 

c) Same question for a 7-digit integer? (where 1424386 --> 1+2+3=6 would now be valid too!)

 

Best,

É.

(now asleep)

 

---

 

Hans H. kindly asked me to be more precise in defining a sound “equation”; we started the following dialog:

 

[HANS] :

Is there anything else in the following 154 "solutions" that should be excluded?

 

 1) 10=10    2) 11=11    3) 12=12    4) 13=13    5) 1+0=1    6) 1+1=2

 7) 1+2=3    8) 1+5=6    9) 1+6=7   10) 15=15   11) 16=16   12) 17=17

13) 1=001   14) 1=0+1   15) 1=1+0   16) 1=1=1   17) 1=+01   18) 19=19

19) 20=20   20) 21=21   21) 22=22   22) 23=23   23) 2+0=2   24) 2+1=3

25) 2+3=5   26) 2+5=7   27) 2+7=9   28) 25=25   29) 26=26   30) 27=27

31) 2=002   32) 2=0+2   33) 2=1+1   34) 2=2+0   35) 2=2=2   36) 2=+02

37) 29=29   38) 30=30   39) 31=31   40) 32=32   41) 33=33   42) 3+0=3

43) 3+2=5   44) 3+3=6   45) 3+6=9   46) 35=35   47) 36=36   48) 37=37

49) 3=003   50) 3=0+3   51) 3=1+2   52) 3=2+1   53) 3=3+0   54) 3=3=3

55) 3=+03   56) 39=39   57) +00=0   58) +01=1   59) +02=2   60) +03=3

(...)

 

[ERIC] :

Hello Hans,

... gee, how fast !

 

> 13) 1=001

> 17) 1=+01

> 57) +00=0

> 58) +01=1

 

... those look awful, don't they?

 

[HANS] :

Could you be a little more explicit about what "true" statements look awful?

 

[ERIC] :

... ouch, this is not easy for me, as I'm not a pro mathematician but only an amateur... Let me see...

Some vocabulary,first:

 

--> k-digit integer:

    an integer written with k concatenated digits (example: 12045 is a 5-digit integer; k=5, here).

 

--> Substitution:

    we note [x+;y=] the substitution of the digit "x" by the symbol "+" inside the k-digit integer and the substitution of the digit "y" by the symbol "=" inside the same k-digit integer. Those substitutions occur simultaneously (example: [4+;8=] asks to replace, inside the k-digit integer, every "4" by a "+" sign and every "8" by a "=" sign. The 5-digit integer 12489 produces, in this example, the string of characters 12+=9).

 

--> Equation:

    the k-digit integer, after [x+;y=], becomes a string of symbols which must be seen as a "classical equation".

 

--> Classical equation:

    an egality where something placed to the left of the sign "=" is arithmetically equal to what is placed on the right of the same "=" sign (examples: 1+3=2+2 or 1+0=1 or 22=22).

 

--> Gertrude Stein notation (“a rose is a rose is a rose”):

    we accept strings with more than one "=" sign, but the resulting equation, though not being "classical", must still say the truth (1=1=1 is valid, 7=5+2=1+6, 9=4+5=9 are valid too)

 

--> Quantity:

    what is placed next to a "+" or next to an "=" sign

 

Rules.

 

Before the substitution:

 

The first digit of a k-digit integer cannot be zero (01234 is forbidden)

 

After the substitution:

 

a) no two "+" signs may follow each other; no two "=" signs either.

b) two substrings are forbidden: "+=" and "=+"

c) no "+" or "=" can start or end a string

d) no quantity can have a leading zero

e) the equation must be true

 

[HANS] :

(...)

We've already decided that the initial digit should not be "0". Let's add the proviso that the initial TWO digits should not be "+0". In addition, let us disallow ANY of the following substrings: {"++", "+00", "+01", "+02", "+03", "+04", "+05", "+06", "+07", "+08", "+09", "=00", "=01", "=02", "=03", "=04", "=05", "=06", "=07", "=08", "=09", "=+0"}. There might be other things we won't like, but let's see what we get so far...

 

Number of 5-digit solutions:

 

=\+      0       1       2       3       4       5       6       7       8

 

1      114

2      116     104

3      118     108     110

4      120     110     110     114

5      120     110     112     114     116

6      122     112     114     114     114     114

7      124     114     116     114     116     116     118

8      126     116     114     116     116     118     120     122

9      128     114     116     118     120     120     122     124     126

 

Maximum (128):

 

  1 1+1=2

  2 1+2=3

  3 1+3=4

  4 1+4=5

  5 1+5=6

  6 1+6=7

  7 1+7=8

  8 11=11

  9 12=12

 10 13=13

 11 14=14

 12 15=15

 13 16=16

 14 17=17

 15 18=18

 16 1=1=1

 17 2+1=3

 18 2+2=4

 19 2+3=5

 20 2+4=6

 21 2+5=7

 22 2+6=8

 23 21=21

 24 22=22

 25 23=23

 26 24=24

 27 25=25

 28 26=26

 29 27=27

 30 28=28

 31 2=1+1

 32 2=2=2

 33 3+1=4

 34 3+2=5

 35 3+3=6

 36 3+4=7

 37 3+5=8

 38 31=31

 39 32=32

 40 33=33

 41 34=34

 42 35=35

 43 36=36

 44 37=37

 45 38=38

 46 3=1+2

 47 3=2+1

 48 3=3=3

 49 4+1=5

 50 4+2=6

 51 4+3=7

 52 4+4=8

 53 41=41

 54 42=42

 55 43=43

 56 44=44

 57 45=45

 58 46=46

 59 47=47

 60 48=48

 61 4=1+3

 62 4=2+2

 63 4=3+1

 64 4=4=4

 65 5+1=6

 66 5+2=7

 67 5+3=8

 68 51=51

 69 52=52

 70 53=53

 71 54=54

 72 55=55

 73 56=56

 74 57=57

 75 58=58

 76 5=1+4

 77 5=2+3

 78 5=3+2

 79 5=4+1

 80 5=5=5

 81 6+1=7

 82 6+2=8

 83 61=61

 84 62=62

 85 63=63

 86 64=64

 87 65=65

 88 66=66

 89 67=67

 90 68=68

 91 6=1+5

 92 6=2+4

 93 6=3+3

 94 6=4+2

 95 6=5+1

 96 6=6=6

 97 7+1=8

 98 71=71

 99 72=72

100 73=73

101 74=74

102 75=75

103 76=76

104 77=77

105 78=78

106 7=1+6

107 7=2+5

108 7=3+4

109 7=4+3

110 7=5+2

111 7=6+1

112 7=7=7

113 81=81

114 82=82

115 83=83

116 84=84

117 85=85

118 86=86

119 87=87

120 88=88

121 8=1+7

122 8=2+6

123 8=3+5

124 8=4+4

125 8=5+3

126 8=6+2

127 8=7+1

128 8=8=8

 

This gives the longest finite sequence of 5-digit integers, the code [0=9+] producing a maximum of 128 terms:

 

S(5) = 10101, 11011, 12012, 13013, 14014, 15015, 16016, 17017, 18018, 19102, 19203, 19304, 19405, 19506, 19607, 19708, 20191, 20202, 21021, 22022, 23023, 24024, 25025, 26026, 27027, 28028, 29103, 29204, 29305, 29406, 29507, 29608, 30192, 30291, 30303, 31031, 32032, 33033, 34034, 35035, 36036, 37037, 38038, 39104, 39205, 39306, 39407, 39508, 40193, 40292, 40391, 40404, 41041, 42042, 43043, 44044, 45045, 46046, 47047, 48048, 49105, 49206, 49307, 49408, 50194, 50293, 50392, 50491, 50505, 51051, 52052, 53053, 54054, 55055, 56056, 57057, 58058, 59106, 59207, 59308, 60195, 60294, 60393, 60492, 60591, 60606, 61061, 62062, 63063, 64064, 65065, 66066, 67067, 68068, 69107, 69208, 70196, 70295, 70394, 70493, 70592, 70691, 70707, 71071, 72072, 73073, 74074, 75075, 76076, 77077, 78078, 79108, 80197, 80296, 80395, 80494, 80593, 80692, 80791, 80808, 81081, 82082, 83083, 84084, 85085, 86086, 87087, 88088.

 

Note that for symmetry reasons the code [9=0+] would also produce a maximum of 128 terms:

 

S’(5) = 10192, 10293, 10394, 10495, 10596, 10697, 10798, 11911, 12912, 13913, 14914, 15915, 16916, 17917, 18918, 19191, 20193, 20294, 20395, 20496, 20597, 20698, 21921, 22922, 23923, 24924, 25925, 26926, 27927, 28928, 29101, 29292, 30194, 30295, 30396, 30497, 30598, 31931, 32932, 33933, 34934, 35935, 36936, 37937, 38938, 39102, 39201, 39393, 40195, 40296, 40397, 40498, 41941, 42942, 43943, 44944, 45945, 46946, 47947, 48948, 49103, 49202, 49301, 49494, 50196, 50297, 50398, 51951, 52952, 53953, 54954, 55955, 56956, 57957, 58958, 59104, 59203, 59302, 59401, 59595, 60197, 60298, 61961, 62962, 63963, 64964, 65965, 66966, 67967, 68968, 69105, 69204, 69303, 69402, 69501, 69696, 70198, 71971, 72972, 73973, 74974, 75975, 76976, 77977, 78978, 79106, 79205, 79304, 79403, 79502, 79601, 79797, 81981, 82982, 83983, 84984, 85985, 86986, 87987, 88988, 89107, 89206, 89305, 89404, 89503, 89602, 89701, 89898.

 

 

Number of 6-digit solutions:

 

=\+      0       1       2       3       4       5       6       7       8

 

1        0

2       54       0

3       52       0      48

4       50       0      46      44

5       48       0      46      44      42

6       48       0      42      42      44      44

7       46       0      42      44      40      42      40

8       44       0      44      42      40      40      36      36

9       42       0      42      40      38      38      36      34      30

 

Maximum (54):

 

 1 11=3+8

 2 11=4+7

 3 11=5+6

 4 11=6+5

 5 11=7+4

 6 11=8+3

 7 13=4+9

 8 13=5+8

 9 13=6+7

10 13=7+6

11 13=8+5

12 13=9+4

13 14=5+9

14 14=6+8

15 14=7+7

16 14=8+6

17 14=9+5

18 15=6+9

19 15=7+8

20 15=8+7

21 15=9+6

22 16=7+9

23 16=8+8

24 16=9+7

25 17=8+9

26 17=9+8

27 18=9+9

28 3+8=11

29 4+7=11

30 4+9=13

31 5+6=11

32 5+8=13

33 5+9=14

34 6+5=11

35 6+7=13

36 6+8=14

37 6+9=15

38 7+4=11

39 7+6=13

40 7+7=14

41 7+8=15

42 7+9=16

43 8+3=11

44 8+5=13

45 8+6=14

46 8+7=15

47 8+8=16

48 8+9=17

49 9+4=13

50 9+5=14

51 9+6=15

52 9+7=16

53 9+8=17

54 9+9=18

 

This gives the longest finite sequence of 6-digit integers, the code [0=2+] producing a maximum of 54 terms:

 

S(6) = 110328, 110427, 110526, 110625, 110724, 110823, 130429, 130528, 130627, 130726, 130825, 130924, 140529, 140628, 140727, 140826, 140925, 150629, 150728, 150827, 150926, 160729, 160828, 160927, 170829, 170928, 180929, 328011, 427011, 429013, 526011, 528013, 529014, 625011, 627013, 628014, 629015, 724011, 726013, 727014, 728015, 729016, 823011, 825013, 826014, 827015, 828016, 829017, 924013, 925014, 926015, 927016, 928017, 929018.

 

Note that for symmetry reasons the code [2=0+] would also produce a maximum of 54 terms:

 

S’(6) = 112308, 112407, 112506, 112605, 112704, 112803, 132409, 132508, 132607, 132706, 132805, 132904, 142509, 142608, 142707, 142806, 142905, 152609, 152708, 152807, 152906, 162709, 162808, 162907, 172809, 172908, 182909, 308211, 407211, 409213, 506211, 508213, 509214, 605211, 607213, 608214, 609215, 704211, 706213, 707214, 708215, 709216, 803211, 805213, 806214, 807215, 808216, 809217, 904213, 905214, 906215, 907216, 908217, 909218.

 

 

Number of 7-digit solutions:

 

=\+      0       1       2       3       4       5       6       7       8

 

1     2423

2     2328    2143

3     2345    2089    2108

4     2364    2104    2004    2156

5     2352    2112    2039    2070    2179

6     2397    2135    2058    2058    2084    2182

7     2418    2154    2095    2084    2099    2121    2232

8     2439    2179    2084    2111    2107    2152    2167    2282

9     2544    2260    2195    2220    2243    2255    2282    2309    2376

 

Maximum (2544):

 

#1 1+1+1=3  #2 1+1+2=4  #3 1+1+3=5  #4 1+1+4=6  #5 1+1+5=7  #6 1+1+6=8  #7 1+11=12  #8 1+12=13  #9 1+13=14  #10 1+14=15  #11 1+15=16  #12 1+16=17  #13 1+17=18  #14 1+1=1+1  #15 1+1=2=2  #16 1+2+1=4  #17 1+2+2=5  #18 1+2+3=6  #19 1+2+4=7  #20 1+2+5=8  #21 1+21=22  #22 1+22=23  #23 1+23=24  #24 1+24=25  #25 1+25=26  #26 1+26=27  #27 1+27=28  #28 1+2=1+2  #29 1+2=2+1  #30 1+2=3=3  #31 1+3+1=5  #32 1+3+2=6  #33 1+3+3=7  #34 1+3+4=8  #35 1+31=32  #36 1+32=33  #37 1+33=34  #38 1+34=35  #39 1+35=36  #40 1+36=37  #41 1+37=38  #42 1+3=1+3  #43 1+3=2+2  #44 1+3=3+1  #45 1+3=4=4  #46 1+4+1=6  #47 1+4+2=7  #48 1+4+3=8  #49 1+41=42  #50 1+42=43  #51 1+43=44  #52 1+44=45  #53 1+45=46  #54 1+46=47  #55 1+47=48  #56 1+4=1+4  #57 1+4=2+3  #58 1+4=3+2  #59 1+4=4+1  #60 1+4=5=5  #61 1+5+1=7  #62 1+5+2=8  #63 1+51=52  #64 1+52=53  #65 1+53=54  #66 1+54=55  #67 1+55=56  #68 1+56=57  #69 1+57=58  #70 1+5=1+5  #71 1+5=2+4  #72 1+5=3+3  #73 1+5=4+2  #74 1+5=5+1  #75 1+5=6=6  #76 1+6+1=8  #77 1+61=62  #78 1+62=63  #79 1+63=64  #80 1+64=65  #81 1+65=66  #82 1+66=67  #83 1+67=68  #84 1+6=1+6  #85 1+6=2+5  #86 1+6=3+4  #87 1+6=4+3  #88 1+6=5+2  #89 1+6=6+1  #90 1+6=7=7  #91 1+71=72  #92 1+72=73  #93 1+73=74  #94 1+74=75  #95 1+75=76  #96 1+76=77  #97 1+77=78  #98 1+7=1+7  #99 1+7=2+6  #100 1+7=3+5  #101 1+7=4+4  #102 1+7=5+3  #103 1+7=6+2  #104 1+7=7+1  #105 1+7=8=8  #106 1+81=82  #107 1+82=83  #108 1+83=84  #109 1+84=85  #110 1+85=86  #111 1+86=87  #112 1+87=88  #113 1+8=1+8  #114 1+8=2+7  #115 1+8=3+6  #116 1+8=4+5  #117 1+8=5+4  #118 1+8=6+3  #119 1+8=7+2  #120 1+8=8+1  #121 11+1=12  #122 11+2=13  #123 11+3=14  #124 11+4=15  #125 11+5=16  #126 11+6=17  #127 11+7=18  #128 111=111  #129 112=112  #130 113=113  #131 114=114  #132 115=115  #133 116=116  #134 117=117  #135 118=118  #136 12+1=13  #137 12+2=14  #138 12+3=15  #139 12+4=16  #140 12+5=17  #141 12+6=18  #142 121=121  #143 122=122  #144 123=123  #145 124=124  #146 125=125  #147 126=126  #148 127=127  #149 128=128  #150 12=1+11  #151 12=11+1  #152 13+1=14  #153 13+2=15  #154 13+3=16  #155 13+4=17  #156 13+5=18  #157 13+8=21  #158 131=131  #159 132=132  #160 133=133  #161 134=134  #162 135=135  #163 136=136  #164 137=137  #165 138=138  #166 13=1+12  #167 13=11+2  #168 13=12+1  #169 13=2+11  #170 14+1=15  #171 14+2=16  #172 14+3=17  #173 14+4=18  #174 14+7=21  #175 14+8=22  #176 141=141  #177 142=142  #178 143=143  #179 144=144  #180 145=145  #181 146=146  #182 147=147  #183 148=148  #184 14=1+13  #185 14=11+3  #186 14=12+2  #187 14=13+1  #188 14=2+12  #189 14=3+11  #190 15+1=16  #191 15+2=17  #192 15+3=18  #193 15+6=21  #194 15+7=22  #195 15+8=23  #196 151=151  #197 152=152  #198 153=153  #199 154=154  #200 155=155  #201 156=156  #202 157=157  #203 158=158  #204 15=1+14  #205 15=11+4  #206 15=12+3  #207 15=13+2  #208 15=14+1  #209 15=2+13  #210 15=3+12  #211 15=4+11  #212 16+1=17  #213 16+2=18  #214 16+5=21  #215 16+6=22  #216 16+7=23  #217 16+8=24  #218 161=161  #219 162=162  #220 163=163  #221 164=164  #222 165=165  #223 166=166  #224 167=167  #225 168=168  #226 16=1+15  #227 16=11+5  #228 16=12+4  #229 16=13+3  #230 16=14+2  #231 16=15+1  #232 16=2+14  #233 16=3+13  #234 16=4+12  #235 16=5+11  #236 17+1=18  #237 17+4=21  #238 17+5=22  #239 17+6=23  #240 17+7=24  #241 17+8=25  #242 171=171  #243 172=172  #244 173=173  #245 174=174  #246 175=175  #247 176=176  #248 177=177  #249 178=178  #250 17=1+16  #251 17=11+6  #252 17=12+5  #253 17=13+4  #254 17=14+3  #255 17=15+2  #256 17=16+1  #257 17=2+15  #258 17=3+14  #259 17=4+13  #260 17=5+12  #261 17=6+11  #262 18+3=21  #263 18+4=22  #264 18+5=23  #265 18+6=24  #266 18+7=25  #267 18+8=26  #268 181=181  #269 182=182  #270 183=183  #271 184=184  #272 185=185  #273 186=186  #274 187=187  #275 188=188  #276 18=1+17  #277 18=11+7  #278 18=12+6  #279 18=13+5  #280 18=14+4  #281 18=15+3  #282 18=16+2  #283 18=17+1  #284 18=2+16  #285 18=3+15  #286 18=4+14  #287 18=5+13  #288 18=6+12  #289 18=7+11  #290 1=1=1=1  #291 2+1+1=4  #292 2+1+2=5  #293 2+1+3=6  #294 2+1+4=7  #295 2+1+5=8  #296 2+11=13  #297 2+12=14  #298 2+13=15  #299 2+14=16  #300 2+15=17  #301 2+16=18  #302 2+1=1+2  #303 2+1=2+1  #304 2+1=3=3  #305 2+2+1=5  #306 2+2+2=6  #307 2+2+3=7  #308 2+2+4=8  #309 2+21=23  #310 2+22=24  #311 2+23=25  #312 2+24=26  #313 2+25=27  #314 2+26=28  #315 2+2=1+3  #316 2+2=2+2  #317 2+2=3+1  #318 2+2=4=4  #319 2+3+1=6  #320 2+3+2=7  #321 2+3+3=8  #322 2+31=33  #323 2+32=34  #324 2+33=35  #325 2+34=36  #326 2+35=37  #327 2+36=38  #328 2+3=1+4  #329 2+3=2+3  #330 2+3=3+2  #331 2+3=4+1  #332 2+3=5=5  #333 2+4+1=7  #334 2+4+2=8  #335 2+41=43  #336 2+42=44  #337 2+43=45  #338 2+44=46  #339 2+45=47  #340 2+46=48  #341 2+4=1+5  #342 2+4=2+4  #343 2+4=3+3  #344 2+4=4+2  #345 2+4=5+1  #346 2+4=6=6  #347 2+5+1=8  #348 2+51=53  #349 2+52=54  #350 2+53=55  #351 2+54=56  #352 2+55=57  #353 2+56=58  #354 2+5=1+6  #355 2+5=2+5  #356 2+5=3+4  #357 2+5=4+3  #358 2+5=5+2  #359 2+5=6+1  #360 2+5=7=7  #361 2+61=63  #362 2+62=64  #363 2+63=65  #364 2+64=66  #365 2+65=67  #366 2+66=68  #367 2+6=1+7  #368 2+6=2+6  #369 2+6=3+5  #370 2+6=4+4  #371 2+6=5+3  #372 2+6=6+2  #373 2+6=7+1  #374 2+6=8=8  #375 2+71=73  #376 2+72=74  #377 2+73=75  #378 2+74=76  #379 2+75=77  #380 2+76=78  #381 2+7=1+8  #382 2+7=2+7  #383 2+7=3+6  #384 2+7=4+5  #385 2+7=5+4  #386 2+7=6+3  #387 2+7=7+2  #388 2+7=8+1  #389 2+81=83  #390 2+82=84  #391 2+83=85  #392 2+84=86  #393 2+85=87  #394 2+86=88  #395 2+8=2+8  #396 2+8=3+7  #397 2+8=4+6  #398 2+8=5+5  #399 2+8=6+4  #400 2+8=7+3  #401 2+8=8+2  #402 21+1=22  #403 21+2=23  #404 21+3=24  #405 21+4=25  #406 21+5=26  #407 21+6=27  #408 21+7=28  #409 211=211  #410 212=212  #411 213=213  #412 214=214  #413 215=215  #414 216=216  #415 217=217  #416 218=218  #417 21=13+8  #418 21=14+7  #419 21=15+6  #420 21=16+5  #421 21=17+4  #422 21=18+3  #423 21=3+18  #424 21=4+17  #425 21=5+16  #426 21=6+15  #427 21=7+14  #428 21=8+13  #429 22+1=23  #430 22+2=24  #431 22+3=25  #432 22+4=26  #433 22+5=27  #434 22+6=28  #435 221=221  #436 222=222  #437 223=223  #438 224=224  #439 225=225  #440 226=226  #441 227=227  #442 228=228  #443 22=1+21  #444 22=14+8  #445 22=15+7  #446 22=16+6  #447 22=17+5  #448 22=18+4  #449 22=21+1  #450 22=4+18  #451 22=5+17  #452 22=6+16  #453 22=7+15  #454 22=8+14  #455 23+1=24  #456 23+2=25  #457 23+3=26  #458 23+4=27  #459 23+5=28  #460 23+8=31  #461 231=231  #462 232=232  #463 233=233  #464 234=234  #465 235=235  #466 236=236  #467 237=237  #468 238=238  #469 23=1+22  #470 23=15+8  #471 23=16+7  #472 23=17+6  #473 23=18+5  #474 23=2+21  #475 23=21+2  #476 23=22+1  #477 23=5+18  #478 23=6+17  #479 23=7+16  #480 23=8+15  #481 24+1=25  #482 24+2=26  #483 24+3=27  #484 24+4=28  #485 24+7=31  #486 24+8=32  #487 241=241  #488 242=242  #489 243=243  #490 244=244  #491 245=245  #492 246=246  #493 247=247  #494 248=248  #495 24=1+23  #496 24=16+8  #497 24=17+7  #498 24=18+6  #499 24=2+22  #500 24=21+3  #501 24=22+2  #502 24=23+1  #503 24=3+21  #504 24=6+18  #505 24=7+17  #506 24=8+16  #507 25+1=26  #508 25+2=27  #509 25+3=28  #510 25+6=31  #511 25+7=32  #512 25+8=33  #513 251=251  #514 252=252  #515 253=253  #516 254=254  #517 255=255  #518 256=256  #519 257=257  #520 258=258  #521 25=1+24  #522 25=17+8  #523 25=18+7  #524 25=2+23  #525 25=21+4  #526 25=22+3  #527 25=23+2  #528 25=24+1  #529 25=3+22  #530 25=4+21  #531 25=7+18  #532 25=8+17  #533 26+1=27  #534 26+2=28  #535 26+5=31  #536 26+6=32  #537 26+7=33  #538 26+8=34  #539 261=261  #540 262=262  #541 263=263  #542 264=264  #543 265=265  #544 266=266  #545 267=267  #546 268=268  #547 26=1+25  #548 26=18+8  #549 26=2+24  #550 26=21+5  #551 26=22+4  #552 26=23+3  #553 26=24+2  #554 26=25+1  #555 26=3+23  #556 26=4+22  #557 26=5+21  #558 26=8+18  #559 27+1=28  #560 27+4=31  #561 27+5=32  #562 27+6=33  #563 27+7=34  #564 27+8=35  #565 271=271  #566 272=272  #567 273=273  #568 274=274  #569 275=275  #570 276=276  #571 277=277  #572 278=278  #573 27=1+26  #574 27=2+25  #575 27=21+6  #576 27=22+5  #577 27=23+4  #578 27=24+3  #579 27=25+2  #580 27=26+1  #581 27=3+24  #582 27=4+23  #583 27=5+22  #584 27=6+21  #585 28+3=31  #586 28+4=32  #587 28+5=33  #588 28+6=34  #589 28+7=35  #590 28+8=36  #591 281=281  #592 282=282  #593 283=283  #594 284=284  #595 285=285  #596 286=286  #597 287=287  #598 288=288  #599 28=1+27  #600 28=2+26  #601 28=21+7  #602 28=22+6  #603 28=23+5  #604 28=24+4  #605 28=25+3  #606 28=26+2  #607 28=27+1  #608 28=3+25  #609 28=4+24  #610 28=5+23  #611 28=6+22  #612 28=7+21  #613 2=1+1=2  #614 2=2=1+1  #615 2=2=2=2  #616 3+1+1=5  #617 3+1+2=6  #618 3+1+3=7  #619 3+1+4=8  #620 3+11=14  #621 3+12=15  #622 3+13=16  #623 3+14=17  #624 3+15=18  #625 3+18=21  #626 3+1=1+3  #627 3+1=2+2  #628 3+1=3+1  #629 3+1=4=4  #630 3+2+1=6  #631 3+2+2=7  #632 3+2+3=8  #633 3+21=24  #634 3+22=25  #635 3+23=26  #636 3+24=27  #637 3+25=28  #638 3+28=31  #639 3+2=1+4  #640 3+2=2+3  #641 3+2=3+2  #642 3+2=4+1  #643 3+2=5=5  #644 3+3+1=7  #645 3+3+2=8  #646 3+31=34  #647 3+32=35  #648 3+33=36  #649 3+34=37  #650 3+35=38  #651 3+38=41  #652 3+3=1+5  #653 3+3=2+4  #654 3+3=3+3  #655 3+3=4+2  #656 3+3=5+1  #657 3+3=6=6  #658 3+4+1=8  #659 3+41=44  #660 3+42=45  #661 3+43=46  #662 3+44=47  #663 3+45=48  #664 3+48=51  #665 3+4=1+6  #666 3+4=2+5  #667 3+4=3+4  #668 3+4=4+3  #669 3+4=5+2  #670 3+4=6+1  #671 3+4=7=7  #672 3+51=54  #673 3+52=55  #674 3+53=56  #675 3+54=57  #676 3+55=58  #677 3+58=61  #678 3+5=1+7  #679 3+5=2+6  #680 3+5=3+5  #681 3+5=4+4  #682 3+5=5+3  #683 3+5=6+2  #684 3+5=7+1  #685 3+5=8=8  #686 3+61=64  #687 3+62=65  #688 3+63=66  #689 3+64=67  #690 3+65=68  #691 3+68=71  #692 3+6=1+8  #693 3+6=2+7  #694 3+6=3+6  #695 3+6=4+5  #696 3+6=5+4  #697 3+6=6+3  #698 3+6=7+2  #699 3+6=8+1  #700 3+71=74  #701 3+72=75  #702 3+73=76  #703 3+74=77  #704 3+75=78  #705 3+78=81  #706 3+7=2+8  #707 3+7=3+7  #708 3+7=4+6  #709 3+7=5+5  #710 3+7=6+4  #711 3+7=7+3  #712 3+7=8+2  #713 3+81=84  #714 3+82=85  #715 3+83=86  #716 3+84=87  #717 3+85=88  #718 3+8=3+8  #719 3+8=4+7  #720 3+8=5+6  #721 3+8=6+5  #722 3+8=7+4  #723 3+8=8+3  #724 31+1=32  #725 31+2=33  #726 31+3=34  #727 31+4=35  #728 31+5=36  #729 31+6=37  #730 31+7=38  #731 311=311  #732 312=312  #733 313=313  #734 314=314  #735 315=315  #736 316=316  #737 317=317  #738 318=318  #739 31=23+8  #740 31=24+7  #741 31=25+6  #742 31=26+5  #743 31=27+4  #744 31=28+3  #745 31=3+28  #746 31=4+27  #747 31=5+26  #748 31=6+25  #749 31=7+24  #750 31=8+23  #751 32+1=33  #752 32+2=34  #753 32+3=35  #754 32+4=36  #755 32+5=37  #756 32+6=38  #757 321=321  #758 322=322  #759 323=323  #760 324=324  #761 325=325  #762 326=326  #763 327=327  #764 328=328  #765 32=1+31  #766 32=24+8  #767 32=25+7  #768 32=26+6  #769 32=27+5  #770 32=28+4  #771 32=31+1  #772 32=4+28  #773 32=5+27  #774 32=6+26  #775 32=7+25  #776 32=8+24  #777 33+1=34  #778 33+2=35  #779 33+3=36  #780 33+4=37  #781 33+5=38  #782 33+8=41  #783 331=331  #784 332=332  #785 333=333  #786 334=334  #787 335=335  #788 336=336  #789 337=337  #790 338=338  #791 33=1+32  #792 33=2+31  #793 33=25+8  #794 33=26+7  #795 33=27+6  #796 33=28+5  #797 33=31+2  #798 33=32+1  #799 33=5+28  #800 33=6+27  #801 33=7+26  #802 33=8+25  #803 34+1=35  #804 34+2=36  #805 34+3=37  #806 34+4=38  #807 34+7=41  #808 34+8=42  #809 341=341  #810 342=342  #811 343=343  #812 344=344  #813 345=345  #814 346=346  #815 347=347  #816 348=348  #817 34=1+33  #818 34=2+32  #819 34=26+8  #820 34=27+7  #821 34=28+6  #822 34=3+31  #823 34=31+3  #824 34=32+2  #825 34=33+1  #826 34=6+28  #827 34=7+27  #828 34=8+26  #829 35+1=36  #830 35+2=37  #831 35+3=38  #832 35+6=41  #833 35+7=42  #834 35+8=43  #835 351=351  #836 352=352  #837 353=353  #838 354=354  #839 355=355  #840 356=356  #841 357=357  #842 358=358  #843 35=1+34  #844 35=2+33  #845 35=27+8  #846 35=28+7  #847 35=3+32  #848 35=31+4  #849 35=32+3  #850 35=33+2  #851 35=34+1  #852 35=4+31  #853 35=7+28  #854 35=8+27  #855 36+1=37  #856 36+2=38  #857 36+5=41  #858 36+6=42  #859 36+7=43  #860 36+8=44  #861 361=361  #862 362=362  #863 363=363  #864 364=364  #865 365=365  #866 366=366  #867 367=367  #868 368=368  #869 36=1+35  #870 36=2+34  #871 36=28+8  #872 36=3+33  #873 36=31+5  #874 36=32+4  #875 36=33+3  #876 36=34+2  #877 36=35+1  #878 36=4+32  #879 36=5+31  #880 36=8+28  #881 37+1=38  #882 37+4=41  #883 37+5=42  #884 37+6=43  #885 37+7=44  #886 37+8=45  #887 371=371  #888 372=372  #889 373=373  #890 374=374  #891 375=375  #892 376=376  #893 377=377  #894 378=378  #895 37=1+36  #896 37=2+35  #897 37=3+34  #898 37=31+6  #899 37=32+5  #900 37=33+4  #901 37=34+3  #902 37=35+2  #903 37=36+1  #904 37=4+33  #905 37=5+32  #906 37=6+31  #907 38+3=41  #908 38+4=42  #909 38+5=43  #910 38+6=44  #911 38+7=45  #912 38+8=46  #913 381=381  #914 382=382  #915 383=383  #916 384=384  #917 385=385  #918 386=386  #919 387=387  #920 388=388  #921 38=1+37  #922 38=2+36  #923 38=3+35  #924 38=31+7  #925 38=32+6  #926 38=33+5  #927 38=34+4  #928 38=35+3  #929 38=36+2  #930 38=37+1  #931 38=4+34  #932 38=5+33  #933 38=6+32  #934 38=7+31  #935 3=1+1+1  #936 3=1+2=3  #937 3=2+1=3  #938 3=3=1+2  #939 3=3=2+1  #940 3=3=3=3  #941 4+1+1=6  #942 4+1+2=7  #943 4+1+3=8  #944 4+11=15  #945 4+12=16  #946 4+13=17  #947 4+14=18  #948 4+17=21  #949 4+18=22  #950 4+1=1+4  #951 4+1=2+3  #952 4+1=3+2  #953 4+1=4+1  #954 4+1=5=5  #955 4+2+1=7  #956 4+2+2=8  #957 4+21=25  #958 4+22=26  #959 4+23=27  #960 4+24=28  #961 4+27=31  #962 4+28=32  #963 4+2=1+5  #964 4+2=2+4  #965 4+2=3+3  #966 4+2=4+2  #967 4+2=5+1  #968 4+2=6=6  #969 4+3+1=8  #970 4+31=35  #971 4+32=36  #972 4+33=37  #973 4+34=38  #974 4+37=41  #975 4+38=42  #976 4+3=1+6  #977 4+3=2+5  #978 4+3=3+4  #979 4+3=4+3  #980 4+3=5+2  #981 4+3=6+1  #982 4+3=7=7  #983 4+41=45  #984 4+42=46  #985 4+43=47  #986 4+44=48  #987 4+47=51  #988 4+48=52  #989 4+4=1+7  #990 4+4=2+6  #991 4+4=3+5  #992 4+4=4+4  #993 4+4=5+3  #994 4+4=6+2  #995 4+4=7+1  #996 4+4=8=8  #997 4+51=55  #998 4+52=56  #999 4+53=57  #1000 4+54=58  #1001 4+57=61  #1002 4+58=62  #1003 4+5=1+8  #1004 4+5=2+7  #1005 4+5=3+6  #1006 4+5=4+5  #1007 4+5=5+4  #1008 4+5=6+3  #1009 4+5=7+2  #1010 4+5=8+1  #1011 4+61=65  #1012 4+62=66  #1013 4+63=67  #1014 4+64=68  #1015 4+67=71  #1016 4+68=72  #1017 4+6=2+8  #1018 4+6=3+7  #1019 4+6=4+6  #1020 4+6=5+5  #1021 4+6=6+4  #1022 4+6=7+3  #1023 4+6=8+2  #1024 4+71=75  #1025 4+72=76  #1026 4+73=77  #1027 4+74=78  #1028 4+77=81  #1029 4+78=82  #1030 4+7=3+8  #1031 4+7=4+7  #1032 4+7=5+6  #1033 4+7=6+5  #1034 4+7=7+4  #1035 4+7=8+3  #1036 4+81=85  #1037 4+82=86  #1038 4+83=87  #1039 4+84=88  #1040 4+8=4+8  #1041 4+8=5+7  #1042 4+8=6+6  #1043 4+8=7+5  #1044 4+8=8+4  #1045 41+1=42  #1046 41+2=43  #1047 41+3=44  #1048 41+4=45  #1049 41+5=46  #1050 41+6=47  #1051 41+7=48  #1052 411=411  #1053 412=412  #1054 413=413  #1055 414=414  #1056 415=415  #1057 416=416  #1058 417=417  #1059 418=418  #1060 41=3+38  #1061 41=33+8  #1062 41=34+7  #1063 41=35+6  #1064 41=36+5  #1065 41=37+4  #1066 41=38+3  #1067 41=4+37  #1068 41=5+36  #1069 41=6+35  #1070 41=7+34  #1071 41=8+33  #1072 42+1=43  #1073 42+2=44  #1074 42+3=45  #1075 42+4=46  #1076 42+5=47  #1077 42+6=48  #1078 421=421  #1079 422=422  #1080 423=423  #1081 424=424  #1082 425=425  #1083 426=426  #1084 427=427  #1085 428=428  #1086 42=1+41  #1087 42=34+8  #1088 42=35+7  #1089 42=36+6  #1090 42=37+5  #1091 42=38+4  #1092 42=4+38  #1093 42=41+1  #1094 42=5+37  #1095 42=6+36  #1096 42=7+35  #1097 42=8+34  #1098 43+1=44  #1099 43+2=45  #1100 43+3=46  #1101 43+4=47  #1102 43+5=48  #1103 43+8=51  #1104 431=431  #1105 432=432  #1106 433=433  #1107 434=434  #1108 435=435  #1109 436=436  #1110 437=437  #1111 438=438  #1112 43=1+42  #1113 43=2+41  #1114 43=35+8  #1115 43=36+7  #1116 43=37+6  #1117 43=38+5  #1118 43=41+2  #1119 43=42+1  #1120 43=5+38  #1121 43=6+37  #1122 43=7+36  #1123 43=8+35  #1124 44+1=45  #1125 44+2=46  #1126 44+3=47  #1127 44+4=48  #1128 44+7=51  #1129 44+8=52  #1130 441=441  #1131 442=442  #1132 443=443  #1133 444=444  #1134 445=445  #1135 446=446  #1136 447=447  #1137 448=448  #1138 44=1+43  #1139 44=2+42  #1140 44=3+41  #1141 44=36+8  #1142 44=37+7  #1143 44=38+6  #1144 44=41+3  #1145 44=42+2  #1146 44=43+1  #1147 44=6+38  #1148 44=7+37  #1149 44=8+36  #1150 45+1=46  #1151 45+2=47  #1152 45+3=48  #1153 45+6=51  #1154 45+7=52  #1155 45+8=53  #1156 451=451  #1157 452=452  #1158 453=453  #1159 454=454  #1160 455=455  #1161 456=456  #1162 457=457  #1163 458=458  #1164 45=1+44  #1165 45=2+43  #1166 45=3+42  #1167 45=37+8  #1168 45=38+7  #1169 45=4+41  #1170 45=41+4  #1171 45=42+3  #1172 45=43+2  #1173 45=44+1  #1174 45=7+38  #1175 45=8+37  #1176 46+1=47  #1177 46+2=48  #1178 46+5=51  #1179 46+6=52  #1180 46+7=53  #1181 46+8=54  #1182 461=461  #1183 462=462  #1184 463=463  #1185 464=464  #1186 465=465  #1187 466=466  #1188 467=467  #1189 468=468  #1190 46=1+45  #1191 46=2+44  #1192 46=3+43  #1193 46=38+8  #1194 46=4+42  #1195 46=41+5  #1196 46=42+4  #1197 46=43+3  #1198 46=44+2  #1199 46=45+1  #1200 46=5+41  #1201 46=8+38  #1202 47+1=48  #1203 47+4=51  #1204 47+5=52  #1205 47+6=53  #1206 47+7=54  #1207 47+8=55  #1208 471=471  #1209 472=472  #1210 473=473  #1211 474=474  #1212 475=475  #1213 476=476  #1214 477=477  #1215 478=478  #1216 47=1+46  #1217 47=2+45  #1218 47=3+44  #1219 47=4+43  #1220 47=41+6  #1221 47=42+5  #1222 47=43+4  #1223 47=44+3  #1224 47=45+2  #1225 47=46+1  #1226 47=5+42  #1227 47=6+41  #1228 48+3=51  #1229 48+4=52  #1230 48+5=53  #1231 48+6=54  #1232 48+7=55  #1233 48+8=56  #1234 481=481  #1235 482=482  #1236 483=483  #1237 484=484  #1238 485=485  #1239 486=486  #1240 487=487  #1241 488=488  #1242 48=1+47  #1243 48=2+46  #1244 48=3+45  #1245 48=4+44  #1246 48=41+7  #1247 48=42+6  #1248 48=43+5  #1249 48=44+4  #1250 48=45+3  #1251 48=46+2  #1252 48=47+1  #1253 48=5+43  #1254 48=6+42  #1255 48=7+41  #1256 4=1+1+2  #1257 4=1+2+1  #1258 4=1+3=4  #1259 4=2+1+1  #1260 4=2+2=4  #1261 4=3+1=4  #1262 4=4=1+3  #1263 4=4=2+2  #1264 4=4=3+1  #1265 4=4=4=4  #1266 5+1+1=7  #1267 5+1+2=8  #1268 5+11=16  #1269 5+12=17  #1270 5+13=18  #1271 5+16=21  #1272 5+17=22  #1273 5+18=23  #1274 5+1=1+5  #1275 5+1=2+4  #1276 5+1=3+3  #1277 5+1=4+2  #1278 5+1=5+1  #1279 5+1=6=6  #1280 5+2+1=8  #1281 5+21=26  #1282 5+22=27  #1283 5+23=28  #1284 5+26=31  #1285 5+27=32  #1286 5+28=33  #1287 5+2=1+6  #1288 5+2=2+5  #1289 5+2=3+4  #1290 5+2=4+3  #1291 5+2=5+2  #1292 5+2=6+1  #1293 5+2=7=7  #1294 5+31=36  #1295 5+32=37  #1296 5+33=38  #1297 5+36=41  #1298 5+37=42  #1299 5+38=43  #1300 5+3=1+7  #1301 5+3=2+6  #1302 5+3=3+5  #1303 5+3=4+4  #1304 5+3=5+3  #1305 5+3=6+2  #1306 5+3=7+1  #1307 5+3=8=8  #1308 5+41=46  #1309 5+42=47  #1310 5+43=48  #1311 5+46=51  #1312 5+47=52  #1313 5+48=53  #1314 5+4=1+8  #1315 5+4=2+7  #1316 5+4=3+6  #1317 5+4=4+5  #1318 5+4=5+4  #1319 5+4=6+3  #1320 5+4=7+2  #1321 5+4=8+1  #1322 5+51=56  #1323 5+52=57  #1324 5+53=58  #1325 5+56=61  #1326 5+57=62  #1327 5+58=63  #1328 5+5=2+8  #1329 5+5=3+7  #1330 5+5=4+6  #1331 5+5=5+5  #1332 5+5=6+4  #1333 5+5=7+3  #1334 5+5=8+2  #1335 5+61=66  #1336 5+62=67  #1337 5+63=68  #1338 5+66=71  #1339 5+67=72  #1340 5+68=73  #1341 5+6=3+8  #1342 5+6=4+7  #1343 5+6=5+6  #1344 5+6=6+5  #1345 5+6=7+4  #1346 5+6=8+3  #1347 5+71=76  #1348 5+72=77  #1349 5+73=78  #1350 5+76=81  #1351 5+77=82  #1352 5+78=83  #1353 5+7=4+8  #1354 5+7=5+7  #1355 5+7=6+6  #1356 5+7=7+5  #1357 5+7=8+4  #1358 5+81=86  #1359 5+82=87  #1360 5+83=88  #1361 5+8=5+8  #1362 5+8=6+7  #1363 5+8=7+6  #1364 5+8=8+5  #1365 51+1=52  #1366 51+2=53  #1367 51+3=54  #1368 51+4=55  #1369 51+5=56  #1370 51+6=57  #1371 51+7=58  #1372 511=511  #1373 512=512  #1374 513=513  #1375 514=514  #1376 515=515  #1377 516=516  #1378 517=517  #1379 518=518  #1380 51=3+48  #1381 51=4+47  #1382 51=43+8  #1383 51=44+7  #1384 51=45+6  #1385 51=46+5  #1386 51=47+4  #1387 51=48+3  #1388 51=5+46  #1389 51=6+45  #1390 51=7+44  #1391 51=8+43  #1392 52+1=53  #1393 52+2=54  #1394 52+3=55  #1395 52+4=56  #1396 52+5=57  #1397 52+6=58  #1398 521=521  #1399 522=522  #1400 523=523  #1401 524=524  #1402 525=525  #1403 526=526  #1404 527=527  #1405 528=528  #1406 52=1+51  #1407 52=4+48  #1408 52=44+8  #1409 52=45+7  #1410 52=46+6  #1411 52=47+5  #1412 52=48+4  #1413 52=5+47  #1414 52=51+1  #1415 52=6+46  #1416 52=7+45  #1417 52=8+44  #1418 53+1=54  #1419 53+2=55  #1420 53+3=56  #1421 53+4=57  #1422 53+5=58  #1423 53+8=61  #1424 531=531  #1425 532=532  #1426 533=533  #1427 534=534  #1428 535=535  #1429 536=536  #1430 537=537  #1431 538=538  #1432 53=1+52  #1433 53=2+51  #1434 53=45+8  #1435 53=46+7  #1436 53=47+6  #1437 53=48+5  #1438 53=5+48  #1439 53=51+2  #1440 53=52+1  #1441 53=6+47  #1442 53=7+46  #1443 53=8+45  #1444 54+1=55  #1445 54+2=56  #1446 54+3=57  #1447 54+4=58  #1448 54+7=61  #1449 54+8=62  #1450 541=541  #1451 542=542  #1452 543=543  #1453 544=544  #1454 545=545  #1455 546=546  #1456 547=547  #1457 548=548  #1458 54=1+53  #1459 54=2+52  #1460 54=3+51  #1461 54=46+8  #1462 54=47+7  #1463 54=48+6  #1464 54=51+3  #1465 54=52+2  #1466 54=53+1  #1467 54=6+48  #1468 54=7+47  #1469 54=8+46  #1470 55+1=56  #1471 55+2=57  #1472 55+3=58  #1473 55+6=61  #1474 55+7=62  #1475 55+8=63  #1476 551=551  #1477 552=552  #1478 553=553  #1479 554=554  #1480 555=555  #1481 556=556  #1482 557=557  #1483 558=558  #1484 55=1+54  #1485 55=2+53  #1486 55=3+52  #1487 55=4+51  #1488 55=47+8  #1489 55=48+7  #1490 55=51+4  #1491 55=52+3  #1492 55=53+2  #1493 55=54+1  #1494 55=7+48  #1495 55=8+47  #1496 56+1=57  #1497 56+2=58  #1498 56+5=61  #1499 56+6=62  #1500 56+7=63  #1501 56+8=64  #1502 561=561  #1503 562=562  #1504 563=563  #1505 564=564  #1506 565=565  #1507 566=566  #1508 567=567  #1509 568=568  #1510 56=1+55  #1511 56=2+54  #1512 56=3+53  #1513 56=4+52  #1514 56=48+8  #1515 56=5+51  #1516 56=51+5  #1517 56=52+4  #1518 56=53+3  #1519 56=54+2  #1520 56=55+1  #1521 56=8+48  #1522 57+1=58  #1523 57+4=61  #1524 57+5=62  #1525 57+6=63  #1526 57+7=64  #1527 57+8=65  #1528 571=571  #1529 572=572  #1530 573=573  #1531 574=574  #1532 575=575  #1533 576=576  #1534 577=577  #1535 578=578  #1536 57=1+56  #1537 57=2+55  #1538 57=3+54  #1539 57=4+53  #1540 57=5+52  #1541 57=51+6  #1542 57=52+5  #1543 57=53+4  #1544 57=54+3  #1545 57=55+2  #1546 57=56+1  #1547 57=6+51  #1548 58+3=61  #1549 58+4=62  #1550 58+5=63  #1551 58+6=64  #1552 58+7=65  #1553 58+8=66  #1554 581=581  #1555 582=582  #1556 583=583  #1557 584=584  #1558 585=585  #1559 586=586  #1560 587=587  #1561 588=588  #1562 58=1+57  #1563 58=2+56  #1564 58=3+55  #1565 58=4+54  #1566 58=5+53  #1567 58=51+7  #1568 58=52+6  #1569 58=53+5  #1570 58=54+4  #1571 58=55+3  #1572 58=56+2  #1573 58=57+1  #1574 58=6+52  #1575 58=7+51  #1576 5=1+1+3  #1577 5=1+2+2  #1578 5=1+3+1  #1579 5=1+4=5  #1580 5=2+1+2  #1581 5=2+2+1  #1582 5=2+3=5  #1583 5=3+1+1  #1584 5=3+2=5  #1585 5=4+1=5  #1586 5=5=1+4  #1587 5=5=2+3  #1588 5=5=3+2  #1589 5=5=4+1  #1590 5=5=5=5  #1591 6+1+1=8  #1592 6+11=17  #1593 6+12=18  #1594 6+15=21  #1595 6+16=22  #1596 6+17=23  #1597 6+18=24  #1598 6+1=1+6  #1599 6+1=2+5  #1600 6+1=3+4  #1601 6+1=4+3  #1602 6+1=5+2  #1603 6+1=6+1  #1604 6+1=7=7  #1605 6+21=27  #1606 6+22=28  #1607 6+25=31  #1608 6+26=32  #1609 6+27=33  #1610 6+28=34  #1611 6+2=1+7  #1612 6+2=2+6  #1613 6+2=3+5  #1614 6+2=4+4  #1615 6+2=5+3  #1616 6+2=6+2  #1617 6+2=7+1  #1618 6+2=8=8  #1619 6+31=37  #1620 6+32=38  #1621 6+35=41  #1622 6+36=42  #1623 6+37=43  #1624 6+38=44  #1625 6+3=1+8  #1626 6+3=2+7  #1627 6+3=3+6  #1628 6+3=4+5  #1629 6+3=5+4  #1630 6+3=6+3  #1631 6+3=7+2  #1632 6+3=8+1  #1633 6+41=47  #1634 6+42=48  #1635 6+45=51  #1636 6+46=52  #1637 6+47=53  #1638 6+48=54  #1639 6+4=2+8  #1640 6+4=3+7  #1641 6+4=4+6  #1642 6+4=5+5  #1643 6+4=6+4  #1644 6+4=7+3  #1645 6+4=8+2  #1646 6+51=57  #1647 6+52=58  #1648 6+55=61  #1649 6+56=62  #1650 6+57=63  #1651 6+58=64  #1652 6+5=3+8  #1653 6+5=4+7  #1654 6+5=5+6  #1655 6+5=6+5  #1656 6+5=7+4  #1657 6+5=8+3  #1658 6+61=67  #1659 6+62=68  #1660 6+65=71  #1661 6+66=72  #1662 6+67=73  #1663 6+68=74  #1664 6+6=4+8  #1665 6+6=5+7  #1666 6+6=6+6  #1667 6+6=7+5  #1668 6+6=8+4  #1669 6+71=77  #1670 6+72=78  #1671 6+75=81  #1672 6+76=82  #1673 6+77=83  #1674 6+78=84  #1675 6+7=5+8  #1676 6+7=6+7  #1677 6+7=7+6  #1678 6+7=8+5  #1679 6+81=87  #1680 6+82=88  #1681 6+8=6+8  #1682 6+8=7+7  #1683 6+8=8+6  #1684 61+1=62  #1685 61+2=63  #1686 61+3=64  #1687 61+4=65  #1688 61+5=66  #1689 61+6=67  #1690 61+7=68  #1691 611=611  #1692 612=612  #1693 613=613  #1694 614=614  #1695 615=615  #1696 616=616  #1697 617=617  #1698 618=618  #1699 61=3+58  #1700 61=4+57  #1701 61=5+56  #1702 61=53+8  #1703 61=54+7  #1704 61=55+6  #1705 61=56+5  #1706 61=57+4  #1707 61=58+3  #1708 61=6+55  #1709 61=7+54  #1710 61=8+53  #1711 62+1=63  #1712 62+2=64  #1713 62+3=65  #1714 62+4=66  #1715 62+5=67  #1716 62+6=68  #1717 621=621  #1718 622=622  #1719 623=623  #1720 624=624  #1721 625=625  #1722 626=626  #1723 627=627  #1724 628=628  #1725 62=1+61  #1726 62=4+58  #1727 62=5+57  #1728 62=54+8  #1729 62=55+7  #1730 62=56+6  #1731 62=57+5  #1732 62=58+4  #1733 62=6+56  #1734 62=61+1  #1735 62=7+55  #1736 62=8+54  #1737 63+1=64  #1738 63+2=65  #1739 63+3=66  #1740 63+4=67  #1741 63+5=68  #1742 63+8=71  #1743 631=631  #1744 632=632  #1745 633=633  #1746 634=634  #1747 635=635  #1748 636=636  #1749 637=637  #1750 638=638  #1751 63=1+62  #1752 63=2+61  #1753 63=5+58  #1754 63=55+8  #1755 63=56+7  #1756 63=57+6  #1757 63=58+5  #1758 63=6+57  #1759 63=61+2  #1760 63=62+1  #1761 63=7+56  #1762 63=8+55  #1763 64+1=65  #1764 64+2=66  #1765 64+3=67  #1766 64+4=68  #1767 64+7=71  #1768 64+8=72  #1769 641=641  #1770 642=642  #1771 643=643  #1772 644=644  #1773 645=645  #1774 646=646  #1775 647=647  #1776 648=648  #1777 64=1+63  #1778 64=2+62  #1779 64=3+61  #1780 64=56+8  #1781 64=57+7  #1782 64=58+6  #1783 64=6+58  #1784 64=61+3  #1785 64=62+2  #1786 64=63+1  #1787 64=7+57  #1788 64=8+56  #1789 65+1=66  #1790 65+2=67  #1791 65+3=68  #1792 65+6=71  #1793 65+7=72  #1794 65+8=73  #1795 651=651  #1796 652=652  #1797 653=653  #1798 654=654  #1799 655=655  #1800 656=656  #1801 657=657  #1802 658=658  #1803 65=1+64  #1804 65=2+63  #1805 65=3+62  #1806 65=4+61  #1807 65=57+8  #1808 65=58+7  #1809 65=61+4  #1810 65=62+3  #1811 65=63+2  #1812 65=64+1  #1813 65=7+58  #1814 65=8+57  #1815 66+1=67  #1816 66+2=68  #1817 66+5=71  #1818 66+6=72  #1819 66+7=73  #1820 66+8=74  #1821 661=661  #1822 662=662  #1823 663=663  #1824 664=664  #1825 665=665  #1826 666=666  #1827 667=667  #1828 668=668  #1829 66=1+65  #1830 66=2+64  #1831 66=3+63  #1832 66=4+62  #1833 66=5+61  #1834 66=58+8  #1835 66=61+5  #1836 66=62+4  #1837 66=63+3  #1838 66=64+2  #1839 66=65+1  #1840 66=8+58  #1841 67+1=68  #1842 67+4=71  #1843 67+5=72  #1844 67+6=73  #1845 67+7=74  #1846 67+8=75  #1847 671=671  #1848 672=672  #1849 673=673  #1850 674=674  #1851 675=675  #1852 676=676  #1853 677=677  #1854 678=678  #1855 67=1+66  #1856 67=2+65  #1857 67=3+64  #1858 67=4+63  #1859 67=5+62  #1860 67=6+61  #1861 67=61+6  #1862 67=62+5  #1863 67=63+4  #1864 67=64+3  #1865 67=65+2  #1866 67=66+1  #1867 68+3=71  #1868 68+4=72  #1869 68+5=73  #1870 68+6=74  #1871 68+7=75  #1872 68+8=76  #1873 681=681  #1874 682=682  #1875 683=683  #1876 684=684  #1877 685=685  #1878 686=686  #1879 687=687  #1880 688=688  #1881 68=1+67  #1882 68=2+66  #1883 68=3+65  #1884 68=4+64  #1885 68=5+63  #1886 68=6+62  #1887 68=61+7  #1888 68=62+6  #1889 68=63+5  #1890 68=64+4  #1891 68=65+3  #1892 68=66+2  #1893 68=67+1  #1894 68=7+61  #1895 6=1+1+4  #1896 6=1+2+3  #1897 6=1+3+2  #1898 6=1+4+1  #1899 6=1+5=6  #1900 6=2+1+3  #1901 6=2+2+2  #1902 6=2+3+1  #1903 6=2+4=6  #1904 6=3+1+2  #1905 6=3+2+1  #1906 6=3+3=6  #1907 6=4+1+1  #1908 6=4+2=6  #1909 6=5+1=6  #1910 6=6=1+5  #1911 6=6=2+4  #1912 6=6=3+3  #1913 6=6=4+2  #1914 6=6=5+1  #1915 6=6=6=6  #1916 7+11=18  #1917 7+14=21  #1918 7+15=22  #1919 7+16=23  #1920 7+17=24  #1921 7+18=25  #1922 7+1=1+7  #1923 7+1=2+6  #1924 7+1=3+5  #1925 7+1=4+4  #1926 7+1=5+3  #1927 7+1=6+2  #1928 7+1=7+1  #1929 7+1=8=8  #1930 7+21=28  #1931 7+24=31  #1932 7+25=32  #1933 7+26=33  #1934 7+27=34  #1935 7+28=35  #1936 7+2=1+8  #1937 7+2=2+7  #1938 7+2=3+6  #1939 7+2=4+5  #1940 7+2=5+4  #1941 7+2=6+3  #1942 7+2=7+2  #1943 7+2=8+1  #1944 7+31=38  #1945 7+34=41  #1946 7+35=42  #1947 7+36=43  #1948 7+37=44  #1949 7+38=45  #1950 7+3=2+8  #1951 7+3=3+7  #1952 7+3=4+6  #1953 7+3=5+5  #1954 7+3=6+4  #1955 7+3=7+3  #1956 7+3=8+2  #1957 7+41=48  #1958 7+44=51  #1959 7+45=52  #1960 7+46=53  #1961 7+47=54  #1962 7+48=55  #1963 7+4=3+8  #1964 7+4=4+7  #1965 7+4=5+6  #1966 7+4=6+5  #1967 7+4=7+4  #1968 7+4=8+3  #1969 7+51=58  #1970 7+54=61  #1971 7+55=62  #1972 7+56=63  #1973 7+57=64  #1974 7+58=65  #1975 7+5=4+8  #1976 7+5=5+7  #1977 7+5=6+6  #1978 7+5=7+5  #1979 7+5=8+4  #1980 7+61=68  #1981 7+64=71  #1982 7+65=72  #1983 7+66=73  #1984 7+67=74  #1985 7+68=75  #1986 7+6=5+8  #1987 7+6=6+7  #1988 7+6=7+6  #1989 7+6=8+5  #1990 7+71=78  #1991 7+74=81  #1992 7+75=82  #1993 7+76=83  #1994 7+77=84  #1995 7+78=85  #1996 7+7=6+8  #1997 7+7=7+7  #1998 7+7=8+6  #1999 7+81=88  #2000 7+8=7+8  #2001 7+8=8+7  #2002 71+1=72  #2003 71+2=73  #2004 71+3=74  #2005 71+4=75  #2006 71+5=76  #2007 71+6=77  #2008 71+7=78  #2009 711=711  #2010 712=712  #2011 713=713  #2012 714=714  #2013 715=715  #2014 716=716  #2015 717=717  #2016 718=718  #2017 71=3+68  #2018 71=4+67  #2019 71=5+66  #2020 71=6+65  #2021 71=63+8  #2022 71=64+7  #2023 71=65+6  #2024 71=66+5  #2025 71=67+4  #2026 71=68+3  #2027 71=7+64  #2028 71=8+63  #2029 72+1=73  #2030 72+2=74  #2031 72+3=75  #2032 72+4=76  #2033 72+5=77  #2034 72+6=78  #2035 721=721  #2036 722=722  #2037 723=723  #2038 724=724  #2039 725=725  #2040 726=726  #2041 727=727  #2042 728=728  #2043 72=1+71  #2044 72=4+68  #2045 72=5+67  #2046 72=6+66  #2047 72=64+8  #2048 72=65+7  #2049 72=66+6  #2050 72=67+5  #2051 72=68+4  #2052 72=7+65  #2053 72=71+1  #2054 72=8+64  #2055 73+1=74  #2056 73+2=75  #2057 73+3=76  #2058 73+4=77  #2059 73+5=78  #2060 73+8=81  #2061 731=731  #2062 732=732  #2063 733=733  #2064 734=734  #2065 735=735  #2066 736=736  #2067 737=737  #2068 738=738  #2069 73=1+72  #2070 73=2+71  #2071 73=5+68  #2072 73=6+67  #2073 73=65+8  #2074 73=66+7  #2075 73=67+6  #2076 73=68+5  #2077 73=7+66  #2078 73=71+2  #2079 73=72+1  #2080 73=8+65  #2081 74+1=75  #2082 74+2=76  #2083 74+3=77  #2084 74+4=78  #2085 74+7=81  #2086 74+8=82  #2087 741=741  #2088 742=742  #2089 743=743  #2090 744=744  #2091 745=745  #2092 746=746  #2093 747=747  #2094 748=748  #2095 74=1+73  #2096 74=2+72  #2097 74=3+71  #2098 74=6+68  #2099 74=66+8  #2100 74=67+7  #2101 74=68+6  #2102 74=7+67  #2103 74=71+3  #2104 74=72+2  #2105 74=73+1  #2106 74=8+66  #2107 75+1=76  #2108 75+2=77  #2109 75+3=78  #2110 75+6=81  #2111 75+7=82  #2112 75+8=83  #2113 751=751  #2114 752=752  #2115 753=753  #2116 754=754  #2117 755=755  #2118 756=756  #2119 757=757  #2120 758=758  #2121 75=1+74  #2122 75=2+73  #2123 75=3+72  #2124 75=4+71  #2125 75=67+8  #2126 75=68+7  #2127 75=7+68  #2128 75=71+4  #2129 75=72+3  #2130 75=73+2  #2131 75=74+1  #2132 75=8+67  #2133 76+1=77  #2134 76+2=78  #2135 76+5=81  #2136 76+6=82  #2137 76+7=83  #2138 76+8=84  #2139 761=761  #2140 762=762  #2141 763=763  #2142 764=764  #2143 765=765  #2144 766=766  #2145 767=767  #2146 768=768  #2147 76=1+75  #2148 76=2+74  #2149 76=3+73  #2150 76=4+72  #2151 76=5+71  #2152 76=68+8  #2153 76=71+5  #2154 76=72+4  #2155 76=73+3  #2156 76=74+2  #2157 76=75+1  #2158 76=8+68  #2159 77+1=78  #2160 77+4=81  #2161 77+5=82  #2162 77+6=83  #2163 77+7=84  #2164 77+8=85  #2165 771=771  #2166 772=772  #2167 773=773  #2168 774=774  #2169 775=775  #2170 776=776  #2171 777=777  #2172 778=778  #2173 77=1+76  #2174 77=2+75  #2175 77=3+74  #2176 77=4+73  #2177 77=5+72  #2178 77=6+71  #2179 77=71+6  #2180 77=72+5  #2181 77=73+4  #2182 77=74+3  #2183 77=75+2  #2184 77=76+1  #2185 78+3=81  #2186 78+4=82  #2187 78+5=83  #2188 78+6=84  #2189 78+7=85  #2190 78+8=86  #2191 781=781  #2192 782=782  #2193 783=783  #2194 784=784  #2195 785=785  #2196 786=786  #2197 787=787  #2198 788=788  #2199 78=1+77  #2200 78=2+76  #2201 78=3+75  #2202 78=4+74  #2203 78=5+73  #2204 78=6+72  #2205 78=7+71  #2206 78=71+7  #2207 78=72+6  #2208 78=73+5  #2209 78=74+4  #2210 78=75+3  #2211 78=76+2  #2212 78=77+1  #2213 7=1+1+5  #2214 7=1+2+4  #2215 7=1+3+3  #2216 7=1+4+2  #2217 7=1+5+1  #2218 7=1+6=7  #2219 7=2+1+4  #2220 7=2+2+3  #2221 7=2+3+2  #2222 7=2+4+1  #2223 7=2+5=7  #2224 7=3+1+3  #2225 7=3+2+2  #2226 7=3+3+1  #2227 7=3+4=7  #2228 7=4+1+2  #2229 7=4+2+1  #2230 7=4+3=7  #2231 7=5+1+1  #2232 7=5+2=7  #2233 7=6+1=7  #2234 7=7=1+6  #2235 7=7=2+5  #2236 7=7=3+4  #2237 7=7=4+3  #2238 7=7=5+2  #2239 7=7=6+1  #2240 7=7=7=7  #2241 8+13=21  #2242 8+14=22  #2243 8+15=23  #2244 8+16=24  #2245 8+17=25  #2246 8+18=26  #2247 8+1=1+8  #2248 8+1=2+7  #2249 8+1=3+6  #2250 8+1=4+5  #2251 8+1=5+4  #2252 8+1=6+3  #2253 8+1=7+2  #2254 8+1=8+1  #2255 8+23=31  #2256 8+24=32  #2257 8+25=33  #2258 8+26=34  #2259 8+27=35  #2260 8+28=36  #2261 8+2=2+8  #2262 8+2=3+7  #2263 8+2=4+6  #2264 8+2=5+5  #2265 8+2=6+4  #2266 8+2=7+3  #2267 8+2=8+2  #2268 8+33=41  #2269 8+34=42  #2270 8+35=43  #2271 8+36=44  #2272 8+37=45  #2273 8+38=46  #2274 8+3=3+8  #2275 8+3=4+7  #2276 8+3=5+6  #2277 8+3=6+5  #2278 8+3=7+4  #2279 8+3=8+3  #2280 8+43=51  #2281 8+44=52  #2282 8+45=53  #2283 8+46=54  #2284 8+47=55  #2285 8+48=56  #2286 8+4=4+8  #2287 8+4=5+7  #2288 8+4=6+6  #2289 8+4=7+5  #2290 8+4=8+4  #2291 8+53=61  #2292 8+54=62  #2293 8+55=63  #2294 8+56=64  #2295 8+57=65  #2296 8+58=66  #2297 8+5=5+8  #2298 8+5=6+7  #2299 8+5=7+6  #2300 8+5=8+5  #2301 8+63=71  #2302 8+64=72  #2303 8+65=73  #2304 8+66=74  #2305 8+67=75  #2306 8+68=76  #2307 8+6=6+8  #2308 8+6=7+7  #2309 8+6=8+6  #2310 8+73=81  #2311 8+74=82  #2312 8+75=83  #2313 8+76=84  #2314 8+77=85  #2315 8+78=86  #2316 8+7=7+8  #2317 8+7=8+7  #2318 8+8=8+8  #2319 81+1=82  #2320 81+2=83  #2321 81+3=84  #2322 81+4=85  #2323 81+5=86  #2324 81+6=87  #2325 81+7=88  #2326 811=811  #2327 812=812  #2328 813=813  #2329 814=814  #2330 815=815  #2331 816=816  #2332 817=817  #2333 818=818  #2334 81=3+78  #2335 81=4+77  #2336 81=5+76  #2337 81=6+75  #2338 81=7+74  #2339 81=73+8  #2340 81=74+7  #2341 81=75+6  #2342 81=76+5  #2343 81=77+4  #2344 81=78+3  #2345 81=8+73  #2346 82+1=83  #2347 82+2=84  #2348 82+3=85  #2349 82+4=86  #2350 82+5=87  #2351 82+6=88  #2352 821=821  #2353 822=822  #2354 823=823  #2355 824=824  #2356 825=825  #2357 826=826  #2358 827=827  #2359 828=828  #2360 82=1+81  #2361 82=4+78  #2362 82=5+77  #2363 82=6+76  #2364 82=7+75  #2365 82=74+8  #2366 82=75+7  #2367 82=76+6  #2368 82=77+5  #2369 82=78+4  #2370 82=8+74  #2371 82=81+1  #2372 83+1=84  #2373 83+2=85  #2374 83+3=86  #2375 83+4=87  #2376 83+5=88  #2377 831=831  #2378 832=832  #2379 833=833  #2380 834=834  #2381 835=835  #2382 836=836  #2383 837=837  #2384 838=838  #2385 83=1+82  #2386 83=2+81  #2387 83=5+78  #2388 83=6+77  #2389 83=7+76  #2390 83=75+8  #2391 83=76+7  #2392 83=77+6  #2393 83=78+5  #2394 83=8+75  #2395 83=81+2  #2396 83=82+1  #2397 84+1=85  #2398 84+2=86  #2399 84+3=87  #2400 84+4=88  #2401 841=841  #2402 842=842  #2403 843=843  #2404 844=844  #2405 845=845  #2406 846=846  #2407 847=847  #2408 848=848  #2409 84=1+83  #2410 84=2+82  #2411 84=3+81  #2412 84=6+78  #2413 84=7+77  #2414 84=76+8  #2415 84=77+7  #2416 84=78+6  #2417 84=8+76  #2418 84=81+3  #2419 84=82+2  #2420 84=83+1  #2421 85+1=86  #2422 85+2=87  #2423 85+3=88  #2424 851=851  #2425 852=852  #2426 853=853  #2427 854=854  #2428 855=855  #2429 856=856  #2430 857=857  #2431 858=858  #2432 85=1+84  #2433 85=2+83  #2434 85=3+82  #2435 85=4+81  #2436 85=7+78  #2437 85=77+8  #2438 85=78+7  #2439 85=8+77  #2440 85=81+4  #2441 85=82+3  #2442 85=83+2  #2443 85=84+1  #2444 86+1=87  #2445 86+2=88  #2446 861=861  #2447 862=862  #2448 863=863  #2449 864=864  #2450 865=865  #2451 866=866  #2452 867=867  #2453 868=868  #2454 86=1+85  #2455 86=2+84  #2456 86=3+83  #2457 86=4+82  #2458 86=5+81  #2459 86=78+8  #2460 86=8+78  #2461 86=81+5  #2462 86=82+4  #2463 86=83+3  #2464 86=84+2  #2465 86=85+1  #2466 87+1=88  #2467 871=871  #2468 872=872  #2469 873=873  #2470 874=874  #2471 875=875  #2472 876=876  #2473 877=877  #2474 878=878  #2475 87=1+86  #2476 87=2+85  #2477 87=3+84  #2478 87=4+83  #2479 87=5+82  #2480 87=6+81  #2481 87=81+6  #2482 87=82+5  #2483 87=83+4  #2484 87=84+3  #2485 87=85+2  #2486 87=86+1  #2487 881=881  #2488 882=882  #2489 883=883  #2490 884=884  #2491 885=885  #2492 886=886  #2493 887=887  #2494 888=888  #2495 88=1+87  #2496 88=2+86  #2497 88=3+85  #2498 88=4+84  #2499 88=5+83  #2500 88=6+82  #2501 88=7+81  #2502 88=81+7  #2503 88=82+6  #2504 88=83+5  #2505 88=84+4  #2506 88=85+3  #2507 88=86+2  #2508 88=87+1  #2509 8=1+1+6  #2510 8=1+2+5  #2511 8=1+3+4  #2512 8=1+4+3  #2513 8=1+5+2  #2514 8=1+6+1  #2515 8=1+7=8  #2516 8=2+1+5  #2517 8=2+2+4  #2518 8=2+3+3  #2519 8=2+4+2  #2520 8=2+5+1  #2521 8=2+6=8  #2522 8=3+1+4  #2523 8=3+2+3  #2524 8=3+3+2  #2525 8=3+4+1  #2526 8=3+5=8  #2527 8=4+1+3  #2528 8=4+2+2  #2529 8=4+3+1  #2530 8=4+4=8  #2531 8=5+1+2  #2532 8=5+2+1  #2533 8=5+3=8  #2534 8=6+1+1  #2535 8=6+2=8  #2536 8=7+1=8  #2537 8=8=1+7  #2538 8=8=2+6  #2539 8=8=3+5  #2540 8=8=4+4  #2541 8=8=5+3  #2542 8=8=6+2  #2543 8=8=7+1  #2544 8=8=8=8

 

This gives the longest finite sequence of 7-digit integers, the code [0=9+] producing a maximum of 2544 terms:

 

S(7) =.1010101, 1110111, 1120112, 1130113, 1140114, 1150115, 1160116, 1170117, 1180118, 1191012, 1192013, 1193014, 1194015, 1195016, 1196017, 1197018, 1201191, 1201911, 1210121, 1220122, 1230123, 1240124, 1250125, 1260126, 1270127, 1280128, 1291013, 1292014, 1293015, 1294016, 1295017, 1296018, 1301192, 1301291, 1301912, 1302911, 1310131, 1320132, 1330133, 1340134, 1350135, 1360136, 1370137, 1380138, 1391014, 1392015, 1393016, 1394017, 1395018, 1398021, 1401193, 1401292, 1401391, 1401913, 1402912, 1403911, 1410141, 1420142, 1430143, 1440144, 1450145, 1460146, 1470147, 1480148, 1491015, 1492016, 1493017, 1494018, 1497021, 1498022, 1501194, 1501293, 1501392, 1501491, 1501914, 1502913, 1503912, 1504911, 1510151, 1520152, 1530153, 1540154, 1550155, 1560156, 1570157, 1580158, 1591016, 1592017, 1593018, 1596021, 1597022, 1598023, 1601195, 1601294, 1601393, 1601492, 1601591, 1601915, 1602914, 1603913, 1604912, 1605911, 1610161, 1620162, 1630163, 1640164, 1650165, 1660166, 1670167, 1680168, 1691017, 1692018, 1695021, 1696022, 1697023, 1698024, 1701196, 1701295, 1701394, 1701493, 1701592, 1701691, 1701916, 1702915, 1703914, 1704913, 1705912, 1706911, 1710171, 1720172, 1730173, 1740174, 1750175, 1760176, 1770177, 1780178, 1791018, 1794021, 1795022, 1796023, 1797024, 1798025, 1801197, 1801296, 1801395, 1801494, 1801593, 1801692, 1801791, 1801917, 1802916, 1803915, 1804914, 1805913, 1806912, 1807911, 1810181, 1820182, 1830183, 1840184, 1850185, 1860186, 1870187, 1880188, 1893021, 1894022, 1895023, 1896024, 1897025, 1898026, 1910191, 1910202, 1911012, 1912013, 1913014, 1914015, 1915016, 1916017, 1917018, 1919103, 1919204, 1919305, 1919406, 1919507, 1919608, 1920192, 1920291, 1920303, 1921022, 1922023, 1923024, 1924025, 1925026, 1926027, 1927028, 1929104, 1929205, 1929306, 1929407, 1929508, 1930193, 1930292, 1930391, 1930404, 1931032, 1932033, 1933034, 1934035, 1935036, 1936037, 1937038, 1939105, 1939206, 1939307, 1939408, 1940194, 1940293, 1940392, 1940491, 1940505, 1941042, 1942043, 1943044, 1944045, 1945046, 1946047, 1947048, 1949106, 1949207, 1949308, 1950195, 1950294, 1950393, 1950492, 1950591, 1950606, 1951052, 1952053, 1953054, 1954055, 1955056, 1956057, 1957058, 1959107, 1959208, 1960196, 1960295, 1960394, 1960493, 1960592, 1960691, 1960707, 1961062, 1962063, 1963064, 1964065, 1965066, 1966067, 1967068, 1969108, 1970197, 1970296, 1970395, 1970494, 1970593, 1970692, 1970791, 1970808, 1971072, 1972073, 1973074, 1974075, 1975076, 1976077, 1977078, 1980198, 1980297, 1980396, 1980495, 1980594, 1980693, 1980792, 1980891, 1981082, 1982083, 1983084, 1984085, 1985086, 1986087, 1987088, 2019102, 2020191, 2020202, 2101398, 2101497, 2101596, 2101695, 2101794, 2101893, 2103918, 2104917, 2105916, 2106915, 2107914, 2108913, 2110211, 2120212, 2130213, 2140214, 2150215, 2160216, 2170217, 2180218, 2191022, 2192023, 2193024, 2194025, 2195026, 2196027, 2197028, 2201498, 2201597, 2201696, 2201795, 2201894, 2201921, 2202191, 2204918, 2205917, 2206916, 2207915, 2208914, 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6956062, 6957063, 6958064, 6960498, 6960597, 6960696, 6960795, 6960894, 6961067, 6962068, 6965071, 6966072, 6967073, 6968074, 6970598, 6970697, 6970796, 6970895, 6971077, 6972078, 6975081, 6976082, 6977083, 6978084, 6980698, 6980797, 6980896, 6981087, 6982088, 7019195, 7019294, 7019393, 7019492, 7019591, 7019607, 7029194, 7029293, 7029392, 7029491, 7029507, 7039193, 7039292, 7039391, 7039407, 7049192, 7049291, 7049307, 7059191, 7059207, 7069107, 7070196, 7070295, 7070394, 7070493, 7070592, 7070691, 7070707, 7103968, 7104967, 7105966, 7106398, 7106497, 7106596, 7106695, 7106794, 7106893, 7106965, 7107964, 7108963, 7110711, 7120712, 7130713, 7140714, 7150715, 7160716, 7170717, 7180718, 7191072, 7192073, 7193074, 7194075, 7195076, 7196077, 7197078, 7201971, 7204968, 7205967, 7206498, 7206597, 7206696, 7206795, 7206894, 7206966, 7207191, 7207965, 7208964, 7210721, 7220722, 7230723, 7240724, 7250725, 7260726, 7270727, 7280728, 7291073, 7292074, 7293075, 7294076, 7295077, 7296078, 7301972, 7302971, 7305968, 7306598, 7306697, 7306796, 7306895, 7306967, 7307192, 7307291, 7307966, 7308965, 7310731, 7320732, 7330733, 7340734, 7350735, 7360736, 7370737, 7380738, 7391074, 7392075, 7393076, 7394077, 7395078, 7398081, 7401973, 7402972, 7403971, 7406698, 7406797, 7406896, 7406968, 7407193, 7407292, 7407391, 7407967, 7408966, 7410741, 7420742, 7430743, 7440744, 7450745, 7460746, 7470747, 7480748, 7491075, 7492076, 7493077, 7494078, 7497081, 7498082, 7501974, 7502973, 7503972, 7504971, 7506798, 7506897, 7507194, 7507293, 7507392, 7507491, 7507968, 7508967, 7510751, 7520752, 7530753, 7540754, 7550755, 7560756, 7570757, 7580758, 7591076, 7592077, 7593078, 7596081, 7597082, 7598083, 7601975, 7602974, 7603973, 7604972, 7605971, 7606898, 7607195, 7607294, 7607393, 7607492, 7607591, 7608968, 7610761, 7620762, 7630763, 7640764, 7650765, 7660766, 7670767, 7680768, 7691077, 7692078, 7695081, 7696082, 7697083, 7698084, 7701976, 7702975, 7703974, 7704973, 7705972, 7706971, 7707196, 7707295, 7707394, 7707493, 7707592, 7707691, 7710771, 7720772, 7730773, 7740774, 7750775, 7760776, 7770777, 7780778, 7791078, 7794081, 7795082, 7796083, 7797084, 7798085, 7801977, 7802976, 7803975, 7804974, 7805973, 7806972, 7807197, 7807296, 7807395, 7807494, 7807593, 7807692, 7807791, 7807971, 7810781, 7820782, 7830783, 7840784, 7850785, 7860786, 7870787, 7880788, 7893081, 7894082, 7895083, 7896084, 7897085, 7898086, 7910197, 7910296, 7910395, 7910494, 7910593, 7910692, 7910791, 7910808, 7911018, 7914021, 7915022, 7916023, 7917024, 7918025, 7920198, 7920297, 7920396, 7920495, 7920594, 7920693, 7920792, 7920891, 7921028, 7924031, 7925032, 7926033, 7927034, 7928035, 7930298, 7930397, 7930496, 7930595, 7930694, 7930793, 7930892, 7931038, 7934041, 7935042, 7936043, 7937044, 7938045, 7940398, 7940497, 7940596, 7940695, 7940794, 7940893, 7941048, 7944051, 7945052, 7946053, 7947054, 7948055, 7950498, 7950597, 7950696, 7950795, 7950894, 7951058, 7954061, 7955062, 7956063, 7957064, 7958065, 7960598, 7960697, 7960796, 7960895, 7961068, 7964071, 7965072, 7966073, 7967074, 7968075, 7970698, 7970797, 7970896, 7971078, 7974081, 7975082, 7976083, 7977084, 7978085, 7980798, 7980897, 7981088, 8019196, 8019295, 8019394, 8019493, 8019592, 8019691, 8019708, 8029195, 8029294, 8029393, 8029492, 8029591, 8029608, 8039194, 8039293, 8039392, 8039491, 8039508, 8049193, 8049292, 8049391, 8049408, 8059192, 8059291, 8059308, 8069191, 8069208, 8079108, 8080197, 8080296, 8080395, 8080494, 8080593, 8080692, 8080791, 8080808., 8103978, 8104977, 8105976, 8106975, 8107398, 8107497, 8107596, 8107695, 8107794, 8107893, 8107974, 8108973, 8110811, 8120812, 8130813, 8140814, 8150815, 8160816, 8170817, 8180818, 8191082, 8192083, 8193084, 8194085, 8195086, 8196087, 8197088, 8201981, 8204978, 8205977, 8206976, 8207498, 8207597, 8207696, 8207795, 8207894, 8207975, 8208191, 8208974, 8210821, 8220822, 8230823, 8240824, 8250825, 8260826, 8270827, 8280828, 8291083, 8292084, 8293085, 8294086, 8295087, 8296088, 8301982, 8302981, 8305978, 8306977, 8307598, 8307697, 8307796, 8307895, 8307976, 8308192, 8308291, 8308975, 8310831, 8320832, 8330833, 8340834, 8350835, 8360836, 8370837, 8380838, 8391084, 8392085, 8393086, 8394087, 8395088, 8401983, 8402982, 8403981, 8406978, 8407698, 8407797, 8407896, 8407977, 8408193, 8408292, 8408391, 8408976, 8410841, 8420842, 8430843, 8440844, 8450845, 8460846, 8470847, 8480848, 8491085, 8492086, 8493087, 8494088, 8501984, 8502983, 8503982, 8504981, 8507798, 8507897, 8507978, 8508194, 8508293, 8508392, 8508491, 8508977, 8510851, 8520852, 8530853, 8540854, 8550855, 8560856, 8570857, 8580858, 8591086, 8592087, 8593088, 8601985, 8602984, 8603983, 8604982, 8605981, 8607898, 8608195, 8608294, 8608393, 8608492, 8608591, 8608978, 8610861, 8620862, 8630863, 8640864, 8650865, 8660866, 8670867, 8680868, 8691087, 8692088, 8701986, 8702985, 8703984, 8704983, 8705982, 8706981, 8708196, 8708295, 8708394, 8708493, 8708592, 8708691, 8710871, 8720872, 8730873, 8740874, 8750875, 8760876, 8770877, 8780878, 8791088, 8801987, 8802986, 8803985, 8804984, 8805983, 8806982, 8807981, 8808197, 8808296, 8808395, 8808494, 8808593, 8808692, 8808791, 8810881, 8820882, 8830883, 8840884, 8850885, 8860886, 8870887, 8880888, 8910198, 8910297, 8910396, 8910495, 8910594, 8910693, 8910792, 8910891, 8913021, 8914022, 8915023, 8916024, 8917025, 8918026, 8920298, 8920397, 8920496, 8920595, 8920694, 8920793, 8920892, 8923031, 8924032, 8925033, 8926034, 8927035, 8928036, 8930398, 8930497, 8930596, 8930695, 8930794, 8930893, 8933041, 8934042, 8935043, 8936044, 8937045, 8938046, 8940498, 8940597, 8940696, 8940795, 8940894, 8943051, 8944052, 8945053, 8946054, 8947055, 8948056, 8950598, 8950697, 8950796, 8950895, 8953061, 8954062, 8955063, 8956064, 8957065, 8958066, 8960698, 8960797, 8960896, 8963071, 8964072, 8965073, 8966074, 8967075, 8968076, 8970798, 8970897, 8973081, 8974082, 8975083, 8976084, 8977085, 8978086, 8980898,

 

Note that for symmetry reasons the code [9=0+] would also produce a maximum of 2544 terms:

 

S’(7) = 1010193, 1010294, 1010395, 1010496, 1010597, 1010698, 1011912, 1012913, 1013914, 1014915, 1015916, 1016917, 1017918, 1019101, 1019292, 1020194, 1020295, 1020396, 1020497, 1020598, 1021922, 1022923, 1023924, 1024925, 1025926, 1026927, 1027928, 1029102, 1029201, 1029393, 1030195, 1030296, 1030397, 1030498, 1031932, 1032933, 1033934, 1034935, 1035936, 1036937, 1037938, 1039103, 1039202, 1039301, 1039494, 1040196, 1040297, 1040398, 1041942, 1042943, 1043944, 1044945, 1045946, 1046947, 1047948, 1049104, 1049203, 1049302, 1049401, 1049595, 1050197, 1050298, 1051952, 1052953, 1053954, 1054955, 1055956, 1056957, 1057958, 1059105, 1059204, 1059303, 1059402, 1059501, 1059696, 1060198, 1061962, 1062963, 1063964, 1064965, 1065966, 1066967, 1067968, 1069106, 1069205, 1069304, 1069403, 1069502, 1069601, 1069797, 1071972, 1072973, 1073974, 1074975, 1075976, 1076977, 1077978, 1079107, 1079206, 1079305, 1079404, 1079503, 1079602, 1079701, 1079898, 1081982, 1082983, 1083984, 1084985, 1085986, 1086987, 1087988, 1089108, 1089207, 1089306, 1089405, 1089504, 1089603, 1089702, 1089801, 1101912, 1102913, 1103914, 1104915, 1105916, 1106917, 1107918, 1119111, 1129112, 1139113, 1149114, 1159115, 1169116, 1179117, 1189118, 1201913, 1202914, 1203915, 1204916, 1205917, 1206918, 1219121, 1229122, 1239123, 1249124, 1259125, 1269126, 1279127, 1289128, 1291011, 1291101, 1301914, 1302915, 1303916, 1304917, 1305918, 1308921, 1319131, 1329132, 1339133, 1349134, 1359135, 1369136, 1379137, 1389138, 1391012, 1391102, 1391201, 1392011, 1401915, 1402916, 1403917, 1404918, 1407921, 1408922, 1419141, 1429142, 1439143, 1449144, 1459145, 1469146, 1479147, 1489148, 1491013, 1491103, 1491202, 1491301, 1492012, 1493011, 1501916, 1502917, 1503918, 1506921, 1507922, 1508923, 1519151, 1529152, 1539153, 1549154, 1559155, 1569156, 1579157, 1589158, 1591014, 1591104, 1591203, 1591302, 1591401, 1592013, 1593012, 1594011, 1601917, 1602918, 1605921, 1606922, 1607923, 1608924, 1619161, 1629162, 1639163, 1649164, 1659165, 1669166, 1679167, 1689168, 1691015, 1691105, 1691204, 1691303, 1691402, 1691501, 1692014, 1693013, 1694012, 1695011, 1701918, 1704921, 1705922, 1706923, 1707924, 1708925, 1719171, 1729172, 1739173, 1749174, 1759175, 1769176, 1779177, 1789178, 1791016, 1791106, 1791205, 1791304, 1791403, 1791502, 1791601, 1792015, 1793014, 1794013, 1795012, 1796011, 1803921, 1804922, 1805923, 1806924, 1807925, 1808926, 1819181, 1829182, 1839183, 1849184, 1859185, 1869186, 1879187, 1889188, 1891017, 1891107, 1891206, 1891305, 1891404, 1891503, 1891602, 1891701, 1892016, 1893015, 1894014, 1895013, 1896012, 1897011, 1919191, 2010194, 2010295, 2010396, 2010497, 2010598, 2011913, 2012914, 2013915, 2014916, 2015917, 2016918, 2019102, 2019201, 2019393, 2020195, 2020296, 2020397, 2020498, 2021923, 2022924, 2023925, 2024926, 2025927, 2026928, 2029103, 2029202, 2029301, 2029494, 2030196, 2030297, 2030398, 2031933, 2032934, 2033935, 2034936, 2035937, 2036938, 2039104, 2039203, 2039302, 2039401, 2039595, 2040197, 2040298, 2041943, 2042944, 2043945, 2044946, 2045947, 2046948, 2049105, 2049204, 2049303, 2049402, 2049501, 2049696, 2050198, 2051953, 2052954, 2053955, 2054956, 2055957, 2056958, 2059106, 2059205, 2059304, 2059403, 2059502, 2059601, 2059797, 2061963, 2062964, 2063965, 2064966, 2065967, 2066968, 2069107, 2069206, 2069305, 2069404, 2069503, 2069602, 2069701, 2069898, 2071973, 2072974, 2073975, 2074976, 2075977, 2076978, 2079108, 2079207, 2079306, 2079405, 2079504, 2079603, 2079702, 2079801, 2081983, 2082984, 2083985, 2084986, 2085987, 2086988, 2089208, 2089307, 2089406, 2089505, 2089604, 2089703, 2089802, 2101922, 2102923, 2103924, 2104925, 2105926, 2106927, 2107928, 2119211, 2129212, 2139213, 2149214, 2159215, 2169216, 2179217, 2189218, 2191308, 2191407, 2191506, 2191605, 2191704, 2191803, 2193018, 2194017, 2195016, 2196015, 2197014, 2198013, 2201923, 2202924, 2203925, 2204926, 2205927, 2206928, 2219221, 2229222, 2239223, 2249224, 2259225, 2269226, 2279227, 2289228, 2291021, 2291408, 2291507, 2291606, 2291705, 2291804, 2292101, 2294018, 2295017, 2296016, 2297015, 2298014, 2301924, 2302925, 2303926, 2304927, 2305928, 2308931, 2319231, 2329232, 2339233, 2349234, 2359235, 2369236, 2379237, 2389238, 2391022, 2391508, 2391607, 2391706, 2391805, 2392021, 2392102, 2392201, 2395018, 2396017, 2397016, 2398015, 2401925, 2402926, 2403927, 2404928, 2407931, 2408932, 2419241, 2429242, 2439243, 2449244, 2459245, 2469246, 2479247, 2489248, 2491023, 2491608, 2491707, 2491806, 2492022, 2492103, 2492202, 2492301, 2493021, 2496018, 2497017, 2498016, 2501926, 2502927, 2503928, 2506931, 2507932, 2508933, 2519251, 2529252, 2539253, 2549254, 2559255, 2569256, 2579257, 2589258, 2591024, 2591708, 2591807, 2592023, 2592104, 2592203, 2592302, 2592401, 2593022, 2594021, 2597018, 2598017, 2601927, 2602928, 2605931, 2606932, 2607933, 2608934, 2619261, 2629262, 2639263, 2649264, 2659265, 2669266, 2679267, 2689268, 2691025, 2691808, 2692024, 2692105, 2692204, 2692303, 2692402, 2692501, 2693023, 2694022, 2695021, 2698018, 2701928, 2704931, 2705932, 2706933, 2707934, 2708935, 2719271, 2729272, 2739273, 2749274, 2759275, 2769276, 2779277, 2789278, 2791026, 2792025, 2792106, 2792205, 2792304, 2792403, 2792502, 2792601, 2793024, 2794023, 2795022, 2796021, 2803931, 2804932, 2805933, 2806934, 2807935, 2808936, 2819281, 2829282, 2839283, 2849284, 2859285, 2869286, 2879287, 2889288, 2891027, 2892026, 2892107, 2892206, 2892305, 2892404, 2892503, 2892602, 2892701, 2893025, 2894024, 2895023, 2896022, 2897021, 2910192, 2929101, 2929292, 3010195, 3010296, 3010397, 3010498, 3011914, 3012915, 3013916, 3014917, 3015918, 3018921, 3019103, 3019202, 3019301, 3019494, 3020196, 3020297, 3020398, 3021924, 3022925, 3023926, 3024927, 3025928, 3028931, 3029104, 3029203, 3029302, 3029401, 3029595, 3030197, 3030298, 3031934, 3032935, 3033936, 3034937, 3035938, 3038941, 3039105, 3039204, 3039303, 3039402, 3039501, 3039696, 3040198, 3041944, 3042945, 3043946, 3044947, 3045948, 3048951, 3049106, 3049205, 3049304, 3049403, 3049502, 3049601, 3049797, 3051954, 3052955, 3053956, 3054957, 3055958, 3058961, 3059107, 3059206, 3059305, 3059404, 3059503, 3059602, 3059701, 3059898, 3061964, 3062965, 3063966, 3064967, 3065968, 3068971, 3069108, 3069207, 3069306, 3069405, 3069504, 3069603, 3069702, 3069801, 3071974, 3072975, 3073976, 3074977, 3075978, 3078981, 3079208, 3079307, 3079406, 3079505, 3079604, 3079703, 3079802, 3081984, 3082985, 3083986, 3084987, 3085988, 3089308, 3089407, 3089506, 3089605, 3089704, 3089803, 3101932, 3102933, 3103934, 3104935, 3105936, 3106937, 3107938, 3119311, 3129312, 3139313, 3149314, 3159315, 3169316, 3179317, 3189318, 3192308, 3192407, 3192506, 3192605, 3192704, 3192803, 3193028, 3194027, 3195026, 3196025, 3197024, 3198023, 3201933, 3202934, 3203935, 3204936, 3205937, 3206938, 3219321, 3229322, 3239323, 3249324, 3259325, 3269326, 3279327, 3289328, 3291031, 3292408, 3292507, 3292606, 3292705, 3292804, 3293101, 3294028, 3295027, 3296026, 3297025, 3298024, 3301934, 3302935, 3303936, 3304937, 3305938, 3308941, 3319331, 3329332, 3339333, 3349334, 3359335, 3369336, 3379337, 3389338, 3391032, 3392031, 3392508, 3392607, 3392706, 3392805, 3393102, 3393201, 3395028, 3396027, 3397026, 3398025, 3401935, 3402936, 3403937, 3404938, 3407941, 3408942, 3419341, 3429342, 3439343, 3449344, 3459345, 3469346, 3479347, 3489348, 3491033, 3492032, 3492608, 3492707, 3492806, 3493031, 3493103, 3493202, 3493301, 3496028, 3497027, 3498026, 3501936, 3502937, 3503938, 3506941, 3507942, 3508943, 3519351, 3529352, 3539353, 3549354, 3559355, 3569356, 3579357, 3589358, 3591034, 3592033, 3592708, 3592807, 3593032, 3593104, 3593203, 3593302, 3593401, 3594031, 3597028, 3598027, 3601937, 3602938, 3605941, 3606942, 3607943, 3608944, 3619361, 3629362, 3639363, 3649364, 3659365, 3669366, 3679367, 3689368, 3691035, 3692034, 3692808, 3693033, 3693105, 3693204, 3693303, 3693402, 3693501, 3694032, 3695031, 3698028, 3701938, 3704941, 3705942, 3706943, 3707944, 3708945, 3719371, 3729372, 3739373, 3749374, 3759375, 3769376, 3779377, 3789378, 3791036, 3792035, 3793034, 3793106, 3793205, 3793304, 3793403, 3793502, 3793601, 3794033, 3795032, 3796031, 3803941, 3804942, 3805943, 3806944, 3807945, 3808946, 3819381, 3829382, 3839383, 3849384, 3859385, 3869386, 3879387, 3889388, 3891037, 3892036, 3893035, 3893107, 3893206, 3893305, 3893404, 3893503, 3893602, 3893701, 3894034, 3895033, 3896032, 3897031, 3910101, 3910293, 3920193, 3939102, 3939201, 3939393, 4010196, 4010297, 4010398, 4011915, 4012916, 4013917, 4014918, 4017921, 4018922, 4019104, 4019203, 4019302, 4019401, 4019595, 4020197, 4020298, 4021925, 4022926, 4023927, 4024928, 4027931, 4028932, 4029105, 4029204, 4029303, 4029402, 4029501, 4029696, 4030198, 4031935, 4032936, 4033937, 4034938, 4037941, 4038942, 4039106, 4039205, 4039304, 4039403, 4039502, 4039601, 4039797, 4041945, 4042946, 4043947, 4044948, 4047951, 4048952, 4049107, 4049206, 4049305, 4049404, 4049503, 4049602, 4049701, 4049898, 4051955, 4052956, 4053957, 4054958, 4057961, 4058962, 4059108, 4059207, 4059306, 4059405, 4059504, 4059603, 4059702, 4059801, 4061965, 4062966, 4063967, 4064968, 4067971, 4068972, 4069208, 4069307, 4069406, 4069505, 4069604, 4069703, 4069802, 4071975, 4072976, 4073977, 4074978, 4077981, 4078982, 4079308, 4079407, 4079506, 4079605, 4079704, 4079803, 4081985, 4082986, 4083987, 4084988, 4089408, 4089507, 4089606, 4089705, 4089804, 4101942, 4102943, 4103944, 4104945, 4105946, 4106947, 4107948, 4119411, 4129412, 4139413, 4149414, 4159415, 4169416, 4179417, 4189418, 4193038, 4193308, 4193407, 4193506, 4193605, 4193704, 4193803, 4194037, 4195036, 4196035, 4197034, 4198033, 4201943, 4202944, 4203945, 4204946, 4205947, 4206948, 4219421, 4229422, 4239423, 4249424, 4259425, 4269426, 4279427, 4289428, 4291041, 4293408, 4293507, 4293606, 4293705, 4293804, 4294038, 4294101, 4295037, 4296036, 4297035, 4298034, 4301944, 4302945, 4303946, 4304947, 4305948, 4308951, 4319431, 4329432, 4339433, 4349434, 4359435, 4369436, 4379437, 4389438, 4391042, 4392041, 4393508, 4393607, 4393706, 4393805, 4394102, 4394201, 4395038, 4396037, 4397036, 4398035, 4401945, 4402946, 4403947, 4404948, 4407951, 4408952, 4419441, 4429442, 4439443, 4449444, 4459445, 4469446, 4479447, 4489448, 4491043, 4492042, 4493041, 4493608, 4493707, 4493806, 4494103, 4494202, 4494301, 4496038, 4497037, 4498036, 4501946, 4502947, 4503948, 4506951, 4507952, 4508953, 4519451, 4529452, 4539453, 4549454, 4559455, 4569456, 4579457, 4589458, 4591044, 4592043, 4593042, 4593708, 4593807, 4594041, 4594104, 4594203, 4594302, 4594401, 4597038, 4598037, 4601947, 4602948, 4605951, 4606952, 4607953, 4608954, 4619461, 4629462, 4639463, 4649464, 4659465, 4669466, 4679467, 4689468, 4691045, 4692044, 4693043, 4693808, 4694042, 4694105, 4694204, 4694303, 4694402, 4694501, 4695041, 4698038, 4701948, 4704951, 4705952, 4706953, 4707954, 4708955, 4719471, 4729472, 4739473, 4749474, 4759475, 4769476, 4779477, 4789478, 4791046, 4792045, 4793044, 4794043, 4794106, 4794205, 4794304, 4794403, 4794502, 4794601, 4795042, 4796041, 4803951, 4804952, 4805953, 4806954, 4807955, 4808956, 4819481, 4829482, 4839483, 4849484, 4859485, 4869486, 4879487, 4889488, 4891047, 4892046, 4893045, 4894044, 4894107, 4894206, 4894305, 4894404, 4894503, 4894602, 4894701, 4895043, 4896042, 4897041, 4910102, 4910201, 4910394, 4920101, 4920294, 4930194, 4949103, 4949202, 4949301, 4949494, 5010197, 5010298, 5011916, 5012917, 5013918, 5016921, 5017922, 5018923, 5019105, 5019204, 5019303, 5019402, 5019501, 5019696, 5020198, 5021926, 5022927, 5023928, 5026931, 5027932, 5028933, 5029106, 5029205, 5029304, 5029403, 5029502, 5029601, 5029797, 5031936, 5032937, 5033938, 5036941, 5037942, 5038943, 5039107, 5039206, 5039305, 5039404, 5039503, 5039602, 5039701, 5039898, 5041946, 5042947, 5043948, 5046951, 5047952, 5048953, 5049108, 5049207, 5049306, 5049405, 5049504, 5049603, 5049702, 5049801, 5051956, 5052957, 5053958, 5056961, 5057962, 5058963, 5059208, 5059307, 5059406, 5059505, 5059604, 5059703, 5059802, 5061966, 5062967, 5063968, 5066971, 5067972, 5068973, 5069308, 5069407, 5069506, 5069605, 5069704, 5069803, 5071976, 5072977, 5073978, 5076981, 5077982, 5078983, 5079408, 5079507, 5079606, 5079705, 5079804, 5081986, 5082987, 5083988, 5089508, 5089607, 5089706, 5089805, 5101952, 5102953, 5103954, 5104955, 5105956, 5106957, 5107958, 5119511, 5129512, 5139513, 5149514, 5159515, 5169516, 5179517, 5189518, 5193048, 5194047, 5194308, 5194407, 5194506, 5194605, 5194704, 5194803, 5195046, 5196045, 5197044, 5198043, 5201953, 5202954, 5203955, 5204956, 5205957, 5206958, 5219521, 5229522, 5239523, 5249524, 5259525, 5269526, 5279527, 5289528, 5291051, 5294048, 5294408, 5294507, 5294606, 5294705, 5294804, 5295047, 5295101, 5296046, 5297045, 5298044, 5301954, 5302955, 5303956, 5304957, 5305958, 5308961, 5319531, 5329532, 5339533, 5349534, 5359535, 5369536, 5379537, 5389538, 5391052, 5392051, 5394508, 5394607, 5394706, 5394805, 5395048, 5395102, 5395201, 5396047, 5397046, 5398045, 5401955, 5402956, 5403957, 5404958, 5407961, 5408962, 5419541, 5429542, 5439543, 5449544, 5459545, 5469546, 5479547, 5489548, 5491053, 5492052, 5493051, 5494608, 5494707, 5494806, 5495103, 5495202, 5495301, 5496048, 5497047, 5498046, 5501956, 5502957, 5503958, 5506961, 5507962, 5508963, 5519551, 5529552, 5539553, 5549554, 5559555, 5569556, 5579557, 5589558, 5591054, 5592053, 5593052, 5594051, 5594708, 5594807, 5595104, 5595203, 5595302, 5595401, 5597048, 5598047, 5601957, 5602958, 5605961, 5606962, 5607963, 5608964, 5619561, 5629562, 5639563, 5649564, 5659565, 5669566, 5679567, 5689568, 5691055, 5692054, 5693053, 5694052, 5694808, 5695051, 5695105, 5695204, 5695303, 5695402, 5695501, 5698048, 5701958, 5704961, 5705962, 5706963, 5707964, 5708965, 5719571, 5729572, 5739573, 5749574, 5759575, 5769576, 5779577, 5789578, 5791056, 5792055, 5793054, 5794053, 5795052, 5795106, 5795205, 5795304, 5795403, 5795502, 5795601, 5796051, 5803961, 5804962, 5805963, 5806964, 5807965, 5808966, 5819581, 5829582, 5839583, 5849584, 5859585, 5869586, 5879587, 5889588, 5891057, 5892056, 5893055, 5894054, 5895053, 5895107, 5895206, 5895305, 5895404, 5895503, 5895602, 5895701, 5896052, 5897051, 5910103, 5910202, 5910301, 5910495, 5920102, 5920201, 5920395, 5930101, 5930295, 5940195, 5959104, 5959203, 5959302, 5959401, 5959595, 6010198, 6011917, 6012918, 6015921, 6016922, 6017923, 6018924, 6019106, 6019205, 6019304, 6019403, 6019502, 6019601, 6019797, 6021927, 6022928, 6025931, 6026932, 6027933, 6028934, 6029107, 6029206, 6029305, 6029404, 6029503, 6029602, 6029701, 6029898, 6031937, 6032938, 6035941, 6036942, 6037943, 6038944, 6039108, 6039207, 6039306, 6039405, 6039504, 6039603, 6039702, 6039801, 6041947, 6042948, 6045951, 6046952, 6047953, 6048954, 6049208, 6049307, 6049406, 6049505, 6049604, 6049703, 6049802, 6051957, 6052958, 6055961, 6056962, 6057963, 6058964, 6059308, 6059407, 6059506, 6059605, 6059704, 6059803, 6061967, 6062968, 6065971, 6066972, 6067973, 6068974, 6069408, 6069507, 6069606, 6069705, 6069804, 6071977, 6072978, 6075981, 6076982, 6077983, 6078984, 6079508, 6079607, 6079706, 6079805, 6081987, 6082988, 6089608, 6089707, 6089806, 6101962, 6102963, 6103964, 6104965, 6105966, 6106967, 6107968, 6119611, 6129612, 6139613, 6149614, 6159615, 6169616, 6179617, 6189618, 6193058, 6194057, 6195056, 6195308, 6195407, 6195506, 6195605, 6195704, 6195803, 6196055, 6197054, 6198053, 6201963, 6202964, 6203965, 6204966, 6205967, 6206968, 6219621, 6229622, 6239623, 6249624, 6259625, 6269626, 6279627, 6289628, 6291061, 6294058, 6295057, 6295408, 6295507, 6295606, 6295705, 6295804, 6296056, 6296101, 6297055, 6298054, 6301964, 6302965, 6303966, 6304967, 6305968, 6308971, 6319631, 6329632, 6339633, 6349634, 6359635, 6369636, 6379637, 6389638, 6391062, 6392061, 6395058, 6395508, 6395607, 6395706, 6395805, 6396057, 6396102, 6396201, 6397056, 6398055, 6401965, 6402966, 6403967, 6404968, 6407971, 6408972, 6419641, 6429642, 6439643, 6449644, 6459645, 6469646, 6479647, 6489648, 6491063, 6492062, 6493061, 6495608, 6495707, 6495806, 6496058, 6496103, 6496202, 6496301, 6497057, 6498056, 6501966, 6502967, 6503968, 6506971, 6507972, 6508973, 6519651, 6529652, 6539653, 6549654, 6559655, 6569656, 6579657, 6589658, 6591064, 6592063, 6593062, 6594061, 6595708, 6595807, 6596104, 6596203, 6596302, 6596401, 6597058, 6598057, 6601967, 6602968, 6605971, 6606972, 6607973, 6608974, 6619661, 6629662, 6639663, 6649664, 6659665, 6669666, 6679667, 6689668, 6691065, 6692064, 6693063, 6694062, 6695061, 6695808, 6696105, 6696204, 6696303, 6696402, 6696501, 6698058, 6701968, 6704971, 6705972, 6706973, 6707974, 6708975, 6719671, 6729672, 6739673, 6749674, 6759675, 6769676, 6779677, 6789678, 6791066, 6792065, 6793064, 6794063, 6795062, 6796061, 6796106, 6796205, 6796304, 6796403, 6796502, 6796601, 6803971, 6804972, 6805973, 6806974, 6807975, 6808976, 6819681, 6829682, 6839683, 6849684, 6859685, 6869686, 6879687, 6889688, 6891067, 6892066, 6893065, 6894064, 6895063, 6896062, 6896107, 6896206, 6896305, 6896404, 6896503, 6896602, 6896701, 6897061, 6910104, 6910203, 6910302, 6910401, 6910596, 6920103, 6920202, 6920301, 6920496, 6930102, 6930201, 6930396, 6940101, 6940296, 6950196, 6969105, 6969204, 6969303, 6969402, 6969501, 6969696, 7011918, 7014921, 7015922, 7016923, 7017924, 7018925, 7019107, 7019206, 7019305, 7019404, 7019503, 7019602, 7019701, 7019898, 7021928, 7024931, 7025932, 7026933, 7027934, 7028935, 7029108, 7029207, 7029306, 7029405, 7029504, 7029603, 7029702, 7029801, 7031938, 7034941, 7035942, 7036943, 7037944, 7038945, 7039208, 7039307, 7039406, 7039505, 7039604, 7039703, 7039802, 7041948, 7044951, 7045952, 7046953, 7047954, 7048955, 7049308, 7049407, 7049506, 7049605, 7049704, 7049803, 7051958, 7054961, 7055962, 7056963, 7057964, 7058965, 7059408, 7059507, 7059606, 7059705, 7059804, 7061968, 7064971, 7065972, 7066973, 7067974, 7068975, 7069508, 7069607, 7069706, 7069805, 7071978, 7074981, 7075982, 7076983, 7077984, 7078985, 7079608, 7079707, 7079806, 7081988, 7089708, 7089807, 7101972, 7102973, 7103974, 7104975, 7105976, 7106977, 7107978, 7119711, 7129712, 7139713, 7149714, 7159715, 7169716, 7179717, 7189718, 7193068, 7194067, 7195066, 7196065, 7196308, 7196407, 7196506, 7196605, 7196704, 7196803, 7197064, 7198063, 7201973, 7202974, 7203975, 7204976, 7205977, 7206978, 7219721, 7229722, 7239723, 7249724, 7259725, 7269726, 7279727, 7289728, 7291071, 7294068, 7295067, 7296066, 7296408, 7296507, 7296606, 7296705, 7296804, 7297065, 7297101, 7298064, 7301974, 7302975, 7303976, 7304977, 7305978, 7308981, 7319731, 7329732, 7339733, 7349734, 7359735, 7369736, 7379737, 7389738, 7391072, 7392071, 7395068, 7396067, 7396508, 7396607, 7396706, 7396805, 7397066, 7397102, 7397201, 7398065, 7401975, 7402976, 7403977, 7404978, 7407981, 7408982, 7419741, 7429742, 7439743, 7449744, 7459745, 7469746, 7479747, 7489748, 7491073, 7492072, 7493071, 7496068, 7496608, 7496707, 7496806, 7497067, 7497103, 7497202, 7497301, 7498066, 7501976, 7502977, 7503978, 7506981, 7507982, 7508983, 7519751, 7529752, 7539753, 7549754, 7559755, 7569756, 7579757, 7589758, 7591074, 7592073, 7593072, 7594071, 7596708, 7596807, 7597068, 7597104, 7597203, 7597302, 7597401, 7598067, 7601977, 7602978, 7605981, 7606982, 7607983, 7608984, 7619761, 7629762, 7639763, 7649764, 7659765, 7669766, 7679767, 7689768, 7691075, 7692074, 7693073, 7694072, 7695071, 7696808, 7697105, 7697204, 7697303, 7697402, 7697501, 7698068, 7701978, 7704981, 7705982, 7706983, 7707984, 7708985, 7719771, 7729772, 7739773, 7749774, 7759775, 7769776, 7779777, 7789778, 7791076, 7792075, 7793074, 7794073, 7795072, 7796071, 7797106, 7797205, 7797304, 7797403, 7797502, 7797601, 7803981, 7804982, 7805983, 7806984, 7807985, 7808986, 7819781, 7829782, 7839783, 7849784, 7859785, 7869786, 7879787, 7889788, 7891077, 7892076, 7893075, 7894074, 7895073, 7896072, 7897071, 7897107, 7897206, 7897305, 7897404, 7897503, 7897602, 7897701, 7910105, 7910204, 7910303, 7910402, 7910501, 7910697, 7920104, 7920203, 7920302, 7920401, 7920597, 7930103, 7930202, 7930301, 7930497, 7940102, 7940201, 7940397, 7950101, 7950297, 7960197, 7979106, 7979205, 7979304, 7979403, 7979502, 7979601, 7979797, 8013921, 8014922, 8015923, 8016924, 8017925, 8018926, 8019108, 8019207, 8019306, 8019405, 8019504, 8019603, 8019702, 8019801, 8023931, 8024932, 8025933, 8026934, 8027935, 8028936, 8029208, 8029307, 8029406, 8029505, 8029604, 8029703, 8029802, 8033941, 8034942, 8035943, 8036944, 8037945, 8038946, 8039308, 8039407, 8039506, 8039605, 8039704, 8039803, 8043951, 8044952, 8045953, 8046954, 8047955, 8048956, 8049408, 8049507, 8049606, 8049705, 8049804, 8053961, 8054962, 8055963, 8056964, 8057965, 8058966, 8059508, 8059607, 8059706, 8059805, 8063971, 8064972, 8065973, 8066974, 8067975, 8068976, 8069608, 8069707, 8069806, 8073981, 8074982, 8075983, 8076984, 8077985, 8078986, 8079708, 8079807, 8089808, 8101982, 8102983, 8103984, 8104985, 8105986, 8106987, 8107988, 8119811, 8129812, 8139813, 8149814, 8159815, 8169816, 8179817, 8189818, 8193078, 8194077, 8195076, 8196075, 8197074, 8197308, 8197407, 8197506, 8197605, 8197704, 8197803, 8198073, 8201983, 8202984, 8203985, 8204986, 8205987, 8206988, 8219821, 8229822, 8239823, 8249824, 8259825, 8269826, 8279827, 8289828, 8291081, 8294078, 8295077, 8296076, 8297075, 8297408, 8297507, 8297606, 8297705, 8297804, 8298074, 8298101, 8301984, 8302985, 8303986, 8304987, 8305988, 8319831, 8329832, 8339833, 8349834, 8359835, 8369836, 8379837, 8389838, 8391082, 8392081, 8395078, 8396077, 8397076, 8397508, 8397607, 8397706, 8397805, 8398075, 8398102, 8398201, 8401985, 8402986, 8403987, 8404988, 8419841, 8429842, 8439843, 8449844, 8459845, 8469846, 8479847, 8489848, 8491083, 8492082, 8493081, 8496078, 8497077, 8497608, 8497707, 8497806, 8498076, 8498103, 8498202, 8498301, 8501986, 8502987, 8503988, 8519851, 8529852, 8539853, 8549854, 8559855, 8569856, 8579857, 8589858, 8591084, 8592083, 8593082, 8594081, 8597078, 8597708, 8597807, 8598077, 8598104, 8598203, 8598302, 8598401, 8601987, 8602988, 8619861, 8629862, 8639863, 8649864, 8659865, 8669866, 8679867, 8689868, 8691085, 8692084, 8693083, 8694082, 8695081, 8697808, 8698078, 8698105, 8698204, 8698303, 8698402, 8698501, 8701988, 8719871, 8729872, 8739873, 8749874, 8759875, 8769876, 8779877, 8789878, 8791086, 8792085, 8793084, 8794083, 8795082, 8796081, 8798106, 8798205, 8798304, 8798403, 8798502, 8798601, 8819881, 8829882, 8839883, 8849884, 8859885, 8869886, 8879887, 8889888, 8891087, 8892086, 8893085, 8894084, 8895083, 8896082, 8897081, 8898107, 8898206, 8898305, 8898404, 8898503, 8898602, 8898701, 8910106, 8910205, 8910304, 8910403, 8910502, 8910601, 8910798, 8920105, 8920204, 8920303, 8920402, 8920501, 8920698, 8930104, 8930203, 8930302, 8930401, 8930598, 8940103, 8940202, 8940301, 8940498, 8950102, 8950201, 8950398, 8960101, 8960298, 8970198, 8989107, 8989206, 8989305, 8989404, 8989503, 8989602, 8989701, 8989898.

 

 

Number of 8-digit solutions:

 

=\+      0       1       2       3       4       5       6       7       8

 

1     1898

2     2766     868

3     3010    1246    2060

4     3118    1404    2182    2402

5     3080    1394    2230    2500    2418

6     3204    1492    2328    2418    2490    2384

7     3294    1588    2386    2438    2532    2564    2556

8     3376    1590    2384    2558    2558    2640    2680    2720

9     3366    1446    2304    2470    2534    2564    2644    2726    2704

 

Hans H.: « A bit of a surprise here: [0+;8=] beats [0+;9=] with ten more solutions. Since they were so close, I've listed both sets, side by side, in the attachment. I thought there might be an easy way to list them with the ten "extra" solutions in [0+;8=] left empty in [0+;9=], instead of all ten at the end of the list. However, it doesn't appear to be a trivial problem to figure out what the ten extra solutions are, in a side-by-side comparison - or, at least I didn't see it in a cursory examination. »

 

Maximum (3376) & Runner-Up (3366):

 

   1 1+1+9=11 1+11=4+8

   2 1+11=3+9 1+11=5+7

   3 1+11=5+7 1+11=6+6

   4 1+11=6+6 1+11=7+5

   5 1+11=7+5 1+11=8+4

   6 1+11=9+3 1+12=5+8

   7 1+12=4+9 1+12=6+7

   8 1+12=6+7 1+12=7+6

   9 1+12=7+6 1+12=8+5

  10 1+12=9+4 1+13=6+8

  11 1+13=5+9 1+13=7+7

  12 1+13=7+7 1+13=8+6

  13 1+13=9+5 1+14=7+8

  14 1+14=6+9 1+14=8+7

  15 1+14=9+6 1+15=8+8

  16 1+15=7+9 1+2+8=11

  17 1+15=9+7 1+3+7=11

  18 1+17=9+9 1+3+8=12

  19 1+2+9=12 1+4+6=11

  20 1+3+7=11 1+4+7=12

  21 1+3+9=13 1+4+8=13

  22 1+4+6=11 1+5+5=11

  23 1+4+7=12 1+5+6=12

  24 1+4+9=14 1+5+7=13

  25 1+5+5=11 1+5+8=14

  26 1+5+6=12 1+6+4=11

  27 1+5+7=13 1+6+5=12

  28 1+5+9=15 1+6+6=13

  29 1+6+4=11 1+6+7=14

  30 1+6+5=12 1+6+8=15

  31 1+6+6=13 1+7+3=11

  32 1+6+7=14 1+7+4=12

  33 1+6+9=16 1+7+5=13

  34 1+7+3=11 1+7+6=14

  35 1+7+4=12 1+7+7=15

  36 1+7+5=13 1+7+8=16

  37 1+7+6=14 1+8+2=11

  38 1+7+7=15 1+8+3=12

  39 1+7+9=17 1+8+4=13

  40 1+9+1=11 1+8+5=14

  41 1+9+2=12 1+8+6=15

  42 1+9+3=13 1+8+7=16

  43 1+9+4=14 1+8+8=17

  44 1+9+5=15 11+11=22

  45 1+9+6=16 11+12=23

  46 1+9+7=17 11+13=24

  47 1+9+9=19 11+14=25

  48 11+11=22 11+15=26

  49 11+12=23 11+16=27

  50 11+13=24 11+17=28

  51 11+14=25 11+1=4+8

  52 11+15=26 11+1=5+7

  53 11+16=27 11+1=6+6

  54 11+1=3+9 11+1=7+5

  55 11+1=5+7 11+1=8+4

  56 11+1=6+6 11+21=32

  57 11+1=7+5 11+22=33

  58 11+1=9+3 11+23=34

  59 11+21=32 11+24=35

  60 11+22=33 11+25=36

  61 11+23=34 11+26=37

  62 11+24=35 11+27=38

  63 11+25=36 11+2=5+8

  64 11+26=37 11+2=6+7

  65 11+2=4+9 11+2=7+6

  66 11+2=6+7 11+2=8+5

  67 11+2=7+6 11+31=42

  68 11+2=9+4 11+32=43

  69 11+31=42 11+33=44

  70 11+32=43 11+34=45

  71 11+33=44 11+35=46

  72 11+34=45 11+36=47

  73 11+35=46 11+37=48

  74 11+36=47 11+3=6+8

  75 11+3=5+9 11+3=7+7

  76 11+3=7+7 11+3=8+6

  77 11+3=9+5 11+41=52

  78 11+41=52 11+42=53

  79 11+42=53 11+43=54

  80 11+43=54 11+44=55

  81 11+44=55 11+45=56

  82 11+45=56 11+46=57

  83 11+46=57 11+47=58

  84 11+4=6+9 11+4=7+8

  85 11+4=9+6 11+4=8+7

  86 11+51=62 11+51=62

  87 11+52=63 11+52=63

  88 11+53=64 11+53=64

  89 11+54=65 11+54=65

  90 11+55=66 11+55=66

  91 11+56=67 11+56=67

  92 11+5=7+9 11+57=68

  93 11+5=9+7 11+5=8+8

  94 11+61=72 11+61=72

  95 11+62=73 11+62=73

  96 11+63=74 11+63=74

  97 11+64=75 11+64=75

  98 11+65=76 11+65=76

  99 11+66=77 11+66=77

 100 11+7=9+9 11+67=78

 101 11=1+1+9 11+71=82

 102 11=1+3+7 11+72=83

 103 11=1+4+6 11+73=84

 104 11=1+5+5 11+74=85

 105 11=1+6+4 11+75=86

 106 11=1+7+3 11+76=87

 107 11=1+9+1 11+77=88

 108 11=11=11 11=1+2+8

 109 11=2+2+7 11=1+3+7

 110 11=2+3+6 11=1+4+6

 111 11=2+4+5 11=1+5+5

 112 11=2+5+4 11=1+6+4

 113 11=2+6+3 11=1+7+3

 114 11=2+7+2 11=1+8+2

 115 11=3+1+7 11=11=11

 116 11=3+2+6 11=2+1+8

 117 11=3+3+5 11=2+2+7

 118 11=3+4+4 11=2+3+6

 119 11=3+5+3 11=2+4+5

 120 11=3+6+2 11=2+5+4

 121 11=3+7+1 11=2+6+3

 122 11=4+1+6 11=2+7+2

 123 11=4+2+5 11=2+8+1

 124 11=4+3+4 11=3+1+7

 125 11=4+4+3 11=3+2+6

 126 11=4+5+2 11=3+3+5

 127 11=4+6+1 11=3+4+4

 128 11=5+1+5 11=3+5+3

 129 11=5+2+4 11=3+6+2

 130 11=5+3+3 11=3+7+1

 131 11=5+4+2 11=4+1+6

 132 11=5+5+1 11=4+2+5

 133 11=6+1+4 11=4+3+4

 134 11=6+2+3 11=4+4+3

 135 11=6+3+2 11=4+5+2

 136 11=6+4+1 11=4+6+1

 137 11=7+1+3 11=5+1+5

 138 11=7+2+2 11=5+2+4

 139 11=7+3+1 11=5+3+3

 140 11=9+1+1 11=5+4+2

 141 12+11=23 11=5+5+1

 142 12+12=24 11=6+1+4

 143 12+13=25 11=6+2+3

 144 12+14=26 11=6+3+2

 145 12+15=27 11=6+4+1

 146 12+17=29 11=7+1+3

 147 12+1=4+9 11=7+2+2

 148 12+1=6+7 11=7+3+1

 149 12+1=7+6 11=8+1+2

 150 12+1=9+4 11=8+2+1

 151 12+19=31 12+11=23

 152 12+21=33 12+12=24

 153 12+22=34 12+13=25

 154 12+23=35 12+14=26

 155 12+24=36 12+15=27

 156 12+25=37 12+16=28

 157 12+27=39 12+1=5+8

 158 12+2=5+9 12+1=6+7

 159 12+2=7+7 12+1=7+6

 160 12+2=9+5 12+1=8+5

 161 12+29=41 12+21=33

 162 12+31=43 12+22=34

 163 12+32=44 12+23=35

 164 12+33=45 12+24=36

 165 12+34=46 12+25=37

 166 12+35=47 12+26=38

 167 12+37=49 12+2=6+8

 168 12+3=6+9 12+2=7+7

 169 12+3=9+6 12+2=8+6

 170 12+39=51 12+31=43

 171 12+41=53 12+32=44

 172 12+42=54 12+33=45

 173 12+43=55 12+34=46

 174 12+44=56 12+35=47

 175 12+45=57 12+36=48

 176 12+47=59 12+3=7+8

 177 12+4=7+9 12+3=8+7

 178 12+4=9+7 12+41=53

 179 12+49=61 12+42=54

 180 12+51=63 12+43=55

 181 12+52=64 12+44=56

 182 12+53=65 12+45=57

 183 12+54=66 12+46=58

 184 12+55=67 12+4=8+8

 185 12+57=69 12+51=63

 186 12+59=71 12+52=64

 187 12+61=73 12+53=65

 188 12+62=74 12+54=66

 189 12+63=75 12+55=67

 190 12+64=76 12+56=68

 191 12+65=77 12+61=73

 192 12+67=79 12+62=74

 193 12+6=9+9 12+63=75

 194 12+79=91 12+64=76

 195 12=1+2+9 12+65=77

 196 12=1+4+7 12+66=78

 197 12=1+5+6 12+71=83

 198 12=1+6+5 12+72=84

 199 12=1+7+4 12+73=85

 200 12=1+9+2 12+74=86

 201 12=12=12 12+75=87

 202 12=2+1+9 12+76=88

 203 12=2+3+7 12=1+3+8

 204 12=2+4+6 12=1+4+7

 205 12=2+5+5 12=1+5+6

 206 12=2+6+4 12=1+6+5

 207 12=2+7+3 12=1+7+4

 208 12=2+9+1 12=1+8+3

 209 12=3+2+7 12=12=12

 210 12=3+3+6 12=2+2+8

 211 12=3+4+5 12=2+3+7

 212 12=3+5+4 12=2+4+6

 213 12=3+6+3 12=2+5+5

 214 12=3+7+2 12=2+6+4

 215 12=4+1+7 12=2+7+3

 216 12=4+2+6 12=2+8+2

 217 12=4+3+5 12=3+1+8

 218 12=4+4+4 12=3+2+7

 219 12=4+5+3 12=3+3+6

 220 12=4+6+2 12=3+4+5

 221 12=4+7+1 12=3+5+4

 222 12=5+1+6 12=3+6+3

 223 12=5+2+5 12=3+7+2

 224 12=5+3+4 12=3+8+1

 225 12=5+4+3 12=4+1+7

 226 12=5+5+2 12=4+2+6

 227 12=5+6+1 12=4+3+5

 228 12=6+1+5 12=4+4+4

 229 12=6+2+4 12=4+5+3

 230 12=6+3+3 12=4+6+2

 231 12=6+4+2 12=4+7+1

 232 12=6+5+1 12=5+1+6

 233 12=7+1+4 12=5+2+5

 234 12=7+2+3 12=5+3+4

 235 12=7+3+2 12=5+4+3

 236 12=7+4+1 12=5+5+2

 237 12=9+1+2 12=5+6+1

 238 12=9+2+1 12=6+1+5

 239 13+11=24 12=6+2+4

 240 13+12=25 12=6+3+3

 241 13+13=26 12=6+4+2

 242 13+14=27 12=6+5+1

 243 13+16=29 12=7+1+4

 244 13+1=5+9 12=7+2+3

 245 13+1=7+7 12=7+3+2

 246 13+1=9+5 12=7+4+1

 247 13+19=32 12=8+1+3

 248 13+21=34 12=8+2+2

 249 13+22=35 12=8+3+1

 250 13+23=36 13+11=24

 251 13+24=37 13+12=25

 252 13+26=39 13+13=26

 253 13+2=6+9 13+14=27

 254 13+2=9+6 13+15=28

 255 13+29=42 13+18=31

 256 13+31=44 13+1=6+8

 257 13+32=45 13+1=7+7

 258 13+33=46 13+1=8+6

 259 13+34=47 13+21=34

 260 13+36=49 13+22=35

 261 13+3=7+9 13+23=36

 262 13+3=9+7 13+24=37

 263 13+39=52 13+25=38

 264 13+41=54 13+28=41

 265 13+42=55 13+2=7+8

 266 13+43=56 13+2=8+7

 267 13+44=57 13+31=44

 268 13+46=59 13+32=45

 269 13+49=62 13+33=46

 270 13+51=64 13+34=47

 271 13+52=65 13+35=48

 272 13+53=66 13+38=51

 273 13+54=67 13+3=8+8

 274 13+56=69 13+41=54

 275 13+5=9+9 13+42=55

 276 13+59=72 13+43=56

 277 13+61=74 13+44=57

 278 13+62=75 13+45=58

 279 13+63=76 13+48=61

 280 13+64=77 13+51=64

 281 13+66=79 13+52=65

 282 13+79=92 13+53=66

 283 13=1+3+9 13+54=67

 284 13=1+5+7 13+55=68

 285 13=1+6+6 13+58=71

 286 13=1+7+5 13+61=74

 287 13=1+9+3 13+62=75

 288 13=13=13 13+63=76

 289 13=2+2+9 13+64=77

 290 13=2+4+7 13+65=78

 291 13=2+5+6 13+68=81

 292 13=2+6+5 13+71=84

 293 13=2+7+4 13+72=85

 294 13=2+9+2 13+73=86

 295 13=3+1+9 13+74=87

 296 13=3+3+7 13+75=88

 297 13=3+4+6 13=1+4+8

 298 13=3+5+5 13=1+5+7

 299 13=3+6+4 13=1+6+6

 300 13=3+7+3 13=1+7+5

 301 13=3+9+1 13=1+8+4

 302 13=4+2+7 13=13=13

 303 13=4+3+6 13=2+3+8

 304 13=4+4+5 13=2+4+7

 305 13=4+5+4 13=2+5+6

 306 13=4+6+3 13=2+6+5

 307 13=4+7+2 13=2+7+4

 308 13=5+1+7 13=2+8+3

 309 13=5+2+6 13=3+2+8

 310 13=5+3+5 13=3+3+7

 311 13=5+4+4 13=3+4+6

 312 13=5+5+3 13=3+5+5

 313 13=5+6+2 13=3+6+4

 314 13=5+7+1 13=3+7+3

 315 13=6+1+6 13=3+8+2

 316 13=6+2+5 13=4+1+8

 317 13=6+3+4 13=4+2+7

 318 13=6+4+3 13=4+3+6

 319 13=6+5+2 13=4+4+5

 320 13=6+6+1 13=4+5+4

 321 13=7+1+5 13=4+6+3

 322 13=7+2+4 13=4+7+2

 323 13=7+3+3 13=4+8+1

 324 13=7+4+2 13=5+1+7

 325 13=7+5+1 13=5+2+6

 326 13=9+1+3 13=5+3+5

 327 13=9+2+2 13=5+4+4

 328 13=9+3+1 13=5+5+3

 329 14+11=25 13=5+6+2

 330 14+12=26 13=5+7+1

 331 14+13=27 13=6+1+6

 332 14+15=29 13=6+2+5

 333 14+17=31 13=6+3+4

 334 14+1=6+9 13=6+4+3

 335 14+1=9+6 13=6+5+2

 336 14+19=33 13=6+6+1

 337 14+21=35 13=7+1+5

 338 14+22=36 13=7+2+4

 339 14+23=37 13=7+3+3

 340 14+25=39 13=7+4+2

 341 14+27=41 13=7+5+1

 342 14+2=7+9 13=8+1+4

 343 14+2=9+7 13=8+2+3

 344 14+29=43 13=8+3+2

 345 14+31=45 13=8+4+1

 346 14+32=46 14+11=25

 347 14+33=47 14+12=26

 348 14+35=49 14+13=27

 349 14+37=51 14+14=28

 350 14+39=53 14+17=31

 351 14+41=55 14+18=32

 352 14+42=56 14+1=7+8

 353 14+43=57 14+1=8+7

 354 14+45=59 14+21=35

 355 14+47=61 14+22=36

 356 14+4=9+9 14+23=37

 357 14+49=63 14+24=38

 358 14+51=65 14+27=41

 359 14+52=66 14+28=42

 360 14+53=67 14+2=8+8

 361 14+55=69 14+31=45

 362 14+57=71 14+32=46

 363 14+59=73 14+33=47

 364 14+61=75 14+34=48

 365 14+62=76 14+37=51

 366 14+63=77 14+38=52

 367 14+65=79 14+41=55

 368 14+77=91 14+42=56

 369 14+79=93 14+43=57

 370 14=1+4+9 14+44=58

 371 14=1+6+7 14+47=61

 372 14=1+7+6 14+48=62

 373 14=1+9+4 14+51=65

 374 14=14=14 14+52=66

 375 14=2+3+9 14+53=67

 376 14=2+5+7 14+54=68

 377 14=2+6+6 14+57=71

 378 14=2+7+5 14+58=72

 379 14=2+9+3 14+61=75

 380 14=3+2+9 14+62=76

 381 14=3+4+7 14+63=77

 382 14=3+5+6 14+64=78

 383 14=3+6+5 14+67=81

 384 14=3+7+4 14+68=82

 385 14=3+9+2 14+71=85

 386 14=4+1+9 14+72=86

 387 14=4+3+7 14+73=87

 388 14=4+4+6 14+74=88

 389 14=4+5+5 14=1+5+8

 390 14=4+6+4 14=1+6+7

 391 14=4+7+3 14=1+7+6

 392 14=4+9+1 14=1+8+5

 393 14=5+2+7 14=14=14

 394 14=5+3+6 14=2+4+8

 395 14=5+4+5 14=2+5+7

 396 14=5+5+4 14=2+6+6

 397 14=5+6+3 14=2+7+5

 398 14=5+7+2 14=2+8+4

 399 14=6+1+7 14=3+3+8

 400 14=6+2+6 14=3+4+7

 401 14=6+3+5 14=3+5+6

 402 14=6+4+4 14=3+6+5

 403 14=6+5+3 14=3+7+4

 404 14=6+6+2 14=3+8+3

 405 14=6+7+1 14=4+2+8

 406 14=7+1+6 14=4+3+7

 407 14=7+2+5 14=4+4+6

 408 14=7+3+4 14=4+5+5

 409 14=7+4+3 14=4+6+4

 410 14=7+5+2 14=4+7+3

 411 14=7+6+1 14=4+8+2

 412 14=9+1+4 14=5+1+8

 413 14=9+2+3 14=5+2+7

 414 14=9+3+2 14=5+3+6

 415 14=9+4+1 14=5+4+5

 416 15+11=26 14=5+5+4

 417 15+12=27 14=5+6+3

 418 15+14=29 14=5+7+2

 419 15+16=31 14=5+8+1

 420 15+17=32 14=6+1+7

 421 15+1=7+9 14=6+2+6

 422 15+1=9+7 14=6+3+5

 423 15+19=34 14=6+4+4

 424 15+21=36 14=6+5+3

 425 15+22=37 14=6+6+2

 426 15+24=39 14=6+7+1

 427 15+26=41 14=7+1+6

 428 15+27=42 14=7+2+5

 429 15+29=44 14=7+3+4

 430 15+31=46 14=7+4+3

 431 15+32=47 14=7+5+2

 432 15+34=49 14=7+6+1

 433 15+36=51 14=8+1+5

 434 15+37=52 14=8+2+4

 435 15+3=9+9 14=8+3+3

 436 15+39=54 14=8+4+2

 437 15+41=56 14=8+5+1

 438 15+42=57 15+11=26

 439 15+44=59 15+12=27

 440 15+46=61 15+13=28

 441 15+47=62 15+16=31

 442 15+49=64 15+17=32

 443 15+51=66 15+18=33

 444 15+52=67 15+1=8+8

 445 15+54=69 15+21=36

 446 15+56=71 15+22=37

 447 15+57=72 15+23=38

 448 15+59=74 15+26=41

 449 15+61=76 15+27=42

 450 15+62=77 15+28=43

 451 15+64=79 15+31=46

 452 15+76=91 15+32=47

 453 15+77=92 15+33=48

 454 15+79=94 15+36=51

 455 15=1+5+9 15+37=52

 456 15=1+7+7 15+38=53

 457 15=1+9+5 15+41=56

 458 15=15=15 15+42=57

 459 15=2+4+9 15+43=58

 460 15=2+6+7 15+46=61

 461 15=2+7+6 15+47=62

 462 15=2+9+4 15+48=63

 463 15=3+3+9 15+51=66

 464 15=3+5+7 15+52=67

 465 15=3+6+6 15+53=68

 466 15=3+7+5 15+56=71

 467 15=3+9+3 15+57=72

 468 15=4+2+9 15+58=73

 469 15=4+4+7 15+61=76

 470 15=4+5+6 15+62=77

 471 15=4+6+5 15+63=78

 472 15=4+7+4 15+66=81

 473 15=4+9+2 15+67=82

 474 15=5+1+9 15+68=83

 475 15=5+3+7 15+71=86

 476 15=5+4+6 15+72=87

 477 15=5+5+5 15+73=88

 478 15=5+6+4 15=1+6+8

 479 15=5+7+3 15=1+7+7

 480 15=5+9+1 15=1+8+6

 481 15=6+2+7 15=15=15

 482 15=6+3+6 15=2+5+8

 483 15=6+4+5 15=2+6+7

 484 15=6+5+4 15=2+7+6

 485 15=6+6+3 15=2+8+5

 486 15=6+7+2 15=3+4+8

 487 15=7+1+7 15=3+5+7

 488 15=7+2+6 15=3+6+6

 489 15=7+3+5 15=3+7+5

 490 15=7+4+4 15=3+8+4

 491 15=7+5+3 15=4+3+8

 492 15=7+6+2 15=4+4+7

 493 15=7+7+1 15=4+5+6

 494 15=9+1+5 15=4+6+5

 495 15=9+2+4 15=4+7+4

 496 15=9+3+3 15=4+8+3

 497 15=9+4+2 15=5+2+8

 498 15=9+5+1 15=5+3+7

 499 16+11=27 15=5+4+6

 500 16+13=29 15=5+5+5

 501 16+15=31 15=5+6+4

 502 16+16=32 15=5+7+3

 503 16+17=33 15=5+8+2

 504 16+19=35 15=6+1+8

 505 16+21=37 15=6+2+7

 506 16+23=39 15=6+3+6

 507 16+25=41 15=6+4+5

 508 16+26=42 15=6+5+4

 509 16+27=43 15=6+6+3

 510 16+2=9+9 15=6+7+2

 511 16+29=45 15=6+8+1

 512 16+31=47 15=7+1+7

 513 16+33=49 15=7+2+6

 514 16+35=51 15=7+3+5

 515 16+36=52 15=7+4+4

 516 16+37=53 15=7+5+3

 517 16+39=55 15=7+6+2

 518 16+41=57 15=7+7+1

 519 16+43=59 15=8+1+6

 520 16+45=61 15=8+2+5

 521 16+46=62 15=8+3+4

 522 16+47=63 15=8+4+3

 523 16+49=65 15=8+5+2

 524 16+51=67 15=8+6+1

 525 16+53=69 16+11=27

 526 16+55=71 16+12=28

 527 16+56=72 16+15=31

 528 16+57=73 16+16=32

 529 16+59=75 16+17=33

 530 16+61=77 16+18=34

 531 16+63=79 16+21=37

 532 16+75=91 16+22=38

 533 16+76=92 16+25=41

 534 16+77=93 16+26=42

 535 16+79=95 16+27=43

 536 16=1+6+9 16+28=44

 537 16=1+9+6 16+31=47

 538 16=16=16 16+32=48

 539 16=2+5+9 16+35=51

 540 16=2+7+7 16+36=52

 541 16=2+9+5 16+37=53

 542 16=3+4+9 16+38=54

 543 16=3+6+7 16+41=57

 544 16=3+7+6 16+42=58

 545 16=3+9+4 16+45=61

 546 16=4+3+9 16+46=62

 547 16=4+5+7 16+47=63

 548 16=4+6+6 16+48=64

 549 16=4+7+5 16+51=67

 550 16=4+9+3 16+52=68

 551 16=5+2+9 16+55=71

 552 16=5+4+7 16+56=72

 553 16=5+5+6 16+57=73

 554 16=5+6+5 16+58=74

 555 16=5+7+4 16+61=77

 556 16=5+9+2 16+62=78

 557 16=6+1+9 16+65=81

 558 16=6+3+7 16+66=82

 559 16=6+4+6 16+67=83

 560 16=6+5+5 16+68=84

 561 16=6+6+4 16+71=87

 562 16=6+7+3 16+72=88

 563 16=6+9+1 16=1+7+8

 564 16=7+2+7 16=1+8+7

 565 16=7+3+6 16=16=16

 566 16=7+4+5 16=2+6+8

 567 16=7+5+4 16=2+7+7

 568 16=7+6+3 16=2+8+6

 569 16=7+7+2 16=3+5+8

 570 16=9+1+6 16=3+6+7

 571 16=9+2+5 16=3+7+6

 572 16=9+3+4 16=3+8+5

 573 16=9+4+3 16=4+4+8

 574 16=9+5+2 16=4+5+7

 575 16=9+6+1 16=4+6+6

 576 17+12=29 16=4+7+5

 577 17+14=31 16=4+8+4

 578 17+15=32 16=5+3+8

 579 17+16=33 16=5+4+7

 580 17+17=34 16=5+5+6

 581 17+1=9+9 16=5+6+5

 582 17+19=36 16=5+7+4

 583 17+22=39 16=5+8+3

 584 17+24=41 16=6+2+8

 585 17+25=42 16=6+3+7

 586 17+26=43 16=6+4+6

 587 17+27=44 16=6+5+5

 588 17+29=46 16=6+6+4

 589 17+32=49 16=6+7+3

 590 17+34=51 16=6+8+2

 591 17+35=52 16=7+1+8

 592 17+36=53 16=7+2+7

 593 17+37=54 16=7+3+6

 594 17+39=56 16=7+4+5

 595 17+42=59 16=7+5+4

 596 17+44=61 16=7+6+3

 597 17+45=62 16=7+7+2

 598 17+46=63 16=7+8+1

 599 17+47=64 16=8+1+7

 600 17+49=66 16=8+2+6

 601 17+52=69 16=8+3+5

 602 17+54=71 16=8+4+4

 603 17+55=72 16=8+5+3

 604 17+56=73 16=8+6+2

 605 17+57=74 16=8+7+1

 606 17+59=76 17+11=28

 607 17+62=79 17+14=31

 608 17+74=91 17+15=32

 609 17+75=92 17+16=33

 610 17+76=93 17+17=34

 611 17+77=94 17+18=35

 612 17+79=96 17+21=38

 613 17=1+7+9 17+24=41

 614 17=1+9+7 17+25=42

 615 17=17=17 17+26=43

 616 17=2+6+9 17+27=44

 617 17=2+9+6 17+28=45

 618 17=3+5+9 17+31=48

 619 17=3+7+7 17+34=51

 620 17=3+9+5 17+35=52

 621 17=4+4+9 17+36=53

 622 17=4+6+7 17+37=54

 623 17=4+7+6 17+38=55

 624 17=4+9+4 17+41=58

 625 17=5+3+9 17+44=61

 626 17=5+5+7 17+45=62

 627 17=5+6+6 17+46=63

 628 17=5+7+5 17+47=64

 629 17=5+9+3 17+48=65

 630 17=6+2+9 17+51=68

 631 17=6+4+7 17+54=71

 632 17=6+5+6 17+55=72

 633 17=6+6+5 17+56=73

 634 17=6+7+4 17+57=74

 635 17=6+9+2 17+58=75

 636 17=7+1+9 17+61=78

 637 17=7+3+7 17+64=81

 638 17=7+4+6 17+65=82

 639 17=7+5+5 17+66=83

 640 17=7+6+4 17+67=84

 641 17=7+7+3 17+68=85

 642 17=7+9+1 17+71=88

 643 17=9+1+7 17=1+8+8

 644 17=9+2+6 17=17=17

 645 17=9+3+5 17=2+7+8

 646 17=9+4+4 17=2+8+7

 647 17=9+5+3 17=3+6+8

 648 17=9+6+2 17=3+7+7

 649 17=9+7+1 17=3+8+6

 650 19+12=31 17=4+5+8

 651 19+13=32 17=4+6+7

 652 19+14=33 17=4+7+6

 653 19+15=34 17=4+8+5

 654 19+16=35 17=5+4+8

 655 19+17=36 17=5+5+7

 656 19+22=41 17=5+6+6

 657 19+23=42 17=5+7+5

 658 19+24=43 17=5+8+4

 659 19+25=44 17=6+3+8

 660 19+26=45 17=6+4+7

 661 19+27=46 17=6+5+6

 662 19+32=51 17=6+6+5

 663 19+33=52 17=6+7+4

 664 19+34=53 17=6+8+3

 665 19+35=54 17=7+2+8

 666 19+36=55 17=7+3+7

 667 19+37=56 17=7+4+6

 668 19+42=61 17=7+5+5

 669 19+43=62 17=7+6+4

 670 19+44=63 17=7+7+3

 671 19+45=64 17=7+8+2

 672 19+46=65 17=8+1+8

 673 19+47=66 17=8+2+7

 674 19+52=71 17=8+3+6

 675 19+53=72 17=8+4+5

 676 19+54=73 17=8+5+4

 677 19+55=74 17=8+6+3

 678 19+56=75 17=8+7+2

 679 19+57=76 17=8+8+1

 680 19+72=91 18+13=31

 681 19+73=92 18+14=32

 682 19+74=93 18+15=33

 683 19+75=94 18+16=34

 684 19+76=95 18+17=35

 685 19+77=96 18+18=36

 686 19=1+9+9 18+23=41

 687 19=19=19 18+24=42

 688 19=3+7+9 18+25=43

 689 19=3+9+7 18+26=44

 690 19=4+6+9 18+27=45

 691 19=4+9+6 18+28=46

 692 19=5+5+9 18+33=51

 693 19=5+7+7 18+34=52

 694 19=5+9+5 18+35=53

 695 19=6+4+9 18+36=54

 696 19=6+6+7 18+37=55

 697 19=6+7+6 18+38=56

 698 19=6+9+4 18+43=61

 699 19=7+3+9 18+44=62

 700 19=7+5+7 18+45=63

 701 19=7+6+6 18+46=64

 702 19=7+7+5 18+47=65

 703 19=7+9+3 18+48=66

 704 19=9+1+9 18+53=71

 705 19=9+3+7 18+54=72

 706 19=9+4+6 18+55=73

 707 19=9+5+5 18+56=74

 708 19=9+6+4 18+57=75

 709 19=9+7+3 18+58=76

 710 19=9+9+1 18+63=81

 711 2+1+9=12 18+64=82

 712 2+11=4+9 18+65=83

 713 2+11=6+7 18+66=84

 714 2+11=7+6 18+67=85

 715 2+11=9+4 18+68=86

 716 2+12=5+9 18=18=18

 717 2+12=7+7 18=2+8+8

 718 2+12=9+5 18=3+7+8

 719 2+13=6+9 18=3+8+7

 720 2+13=9+6 18=4+6+8

 721 2+14=7+9 18=4+7+7

 722 2+14=9+7 18=4+8+6

 723 2+16=9+9 18=5+5+8

 724 2+2+7=11 18=5+6+7

 725 2+2+9=13 18=5+7+6

 726 2+3+6=11 18=5+8+5

 727 2+3+7=12 18=6+4+8

 728 2+3+9=14 18=6+5+7

 729 2+4+5=11 18=6+6+6

 730 2+4+6=12 18=6+7+5

 731 2+4+7=13 18=6+8+4

 732 2+4+9=15 18=7+3+8

 733 2+5+4=11 18=7+4+7

 734 2+5+5=12 18=7+5+6

 735 2+5+6=13 18=7+6+5

 736 2+5+7=14 18=7+7+4

 737 2+5+9=16 18=7+8+3

 738 2+6+3=11 18=8+2+8

 739 2+6+4=12 18=8+3+7

 740 2+6+5=13 18=8+4+6

 741 2+6+6=14 18=8+5+5

 742 2+6+7=15 18=8+6+4

 743 2+6+9=17 18=8+7+3

 744 2+7+2=11 18=8+8+2

 745 2+7+3=12 2+1+8=11

 746 2+7+4=13 2+11=5+8

 747 2+7+5=14 2+11=6+7

 748 2+7+6=15 2+11=7+6

 749 2+7+7=16 2+11=8+5

 750 2+9+1=12 2+12=6+8

 751 2+9+2=13 2+12=7+7

 752 2+9+3=14 2+12=8+6

 753 2+9+4=15 2+13=7+8

 754 2+9+5=16 2+13=8+7

 755 2+9+6=17 2+14=8+8

 756 21+11=32 2+2+7=11

 757 21+12=33 2+2+8=12

 758 21+13=34 2+3+6=11

 759 21+14=35 2+3+7=12

 760 21+15=36 2+3+8=13

 761 21+16=37 2+4+5=11

 762 21+21=42 2+4+6=12

 763 21+22=43 2+4+7=13

 764 21+23=44 2+4+8=14

 765 21+24=45 2+5+4=11

 766 21+25=46 2+5+5=12

 767 21+26=47 2+5+6=13

 768 21+31=52 2+5+7=14

 769 21+32=53 2+5+8=15

 770 21+33=54 2+6+3=11

 771 21+34=55 2+6+4=12

 772 21+35=56 2+6+5=13

 773 21+36=57 2+6+6=14

 774 21+41=62 2+6+7=15

 775 21+42=63 2+6+8=16

 776 21+43=64 2+7+2=11

 777 21+44=65 2+7+3=12

 778 21+45=66 2+7+4=13

 779 21+46=67 2+7+5=14

 780 21+51=72 2+7+6=15

 781 21+52=73 2+7+7=16

 782 21+53=74 2+7+8=17

 783 21+54=75 2+8+1=11

 784 21+55=76 2+8+2=12

 785 21+56=77 2+8+3=13

 786 21+71=92 2+8+4=14

 787 21+72=93 2+8+5=15

 788 21+73=94 2+8+6=16

 789 21+74=95 2+8+7=17

 790 21+75=96 2+8+8=18

 791 21+76=97 21+11=32

 792 21=21=21 21+12=33

 793 21=3+9+9 21+13=34

 794 21=5+7+9 21+14=35

 795 21=5+9+7 21+15=36

 796 21=6+6+9 21+16=37

 797 21=6+9+6 21+17=38

 798 21=7+5+9 21+21=42

 799 21=7+7+7 21+22=43

 800 21=7+9+5 21+23=44

 801 21=9+3+9 21+24=45

 802 21=9+5+7 21+25=46

 803 21=9+6+6 21+26=47

 804 21=9+7+5 21+27=48

 805 21=9+9+3 21+31=52

 806 22+11=33 21+32=53

 807 22+12=34 21+33=54

 808 22+13=35 21+34=55

 809 22+14=36 21+35=56

 810 22+15=37 21+36=57

 811 22+17=39 21+37=58

 812 22+19=41 21+41=62

 813 22+21=43 21+42=63

 814 22+22=44 21+43=64

 815 22+23=45 21+44=65

 816 22+24=46 21+45=66

 817 22+25=47 21+46=67

 818 22+27=49 21+47=68

 819 22+29=51 21+51=72

 820 22+31=53 21+52=73

 821 22+32=54 21+53=74

 822 22+33=55 21+54=75

 823 22+34=56 21+55=76

 824 22+35=57 21+56=77

 825 22+37=59 21+57=78

 826 22+39=61 21+61=82

 827 22+41=63 21+62=83

 828 22+42=64 21+63=84

 829 22+43=65 21+64=85

 830 22+44=66 21+65=86

 831 22+45=67 21+66=87

 832 22+47=69 21+67=88

 833 22+49=71 21=21=21

 834 22+51=73 21=5+8+8

 835 22+52=74 21=6+7+8

 836 22+53=75 21=6+8+7

 837 22+54=76 21=7+6+8

 838 22+55=77 21=7+7+7

 839 22+57=79 21=7+8+6

 840 22+69=91 21=8+5+8

 841 22+71=93 21=8+6+7

 842 22+72=94 21=8+7+6

 843 22+73=95 21=8+8+5

 844 22+74=96 22+11=33

 845 22+75=97 22+12=34

 846 22+77=99 22+13=35

 847 22=11+11 22+14=36

 848 22=22=22 22+15=37

 849 22=4+9+9 22+16=38

 850 22=6+7+9 22+21=43

 851 22=6+9+7 22+22=44

 852 22=7+6+9 22+23=45

 853 22=7+9+6 22+24=46

 854 22=9+4+9 22+25=47

 855 22=9+6+7 22+26=48

 856 22=9+7+6 22+31=53

 857 22=9+9+4 22+32=54

 858 23+11=34 22+33=55

 859 23+12=35 22+34=56

 860 23+13=36 22+35=57

 861 23+14=37 22+36=58

 862 23+16=39 22+41=63

 863 23+19=42 22+42=64

 864 23+21=44 22+43=65

 865 23+22=45 22+44=66

 866 23+23=46 22+45=67

 867 23+24=47 22+46=68

 868 23+26=49 22+51=73

 869 23+29=52 22+52=74

 870 23+31=54 22+53=75

 871 23+32=55 22+54=76

 872 23+33=56 22+55=77

 873 23+34=57 22+56=78

 874 23+36=59 22+61=83

 875 23+39=62 22+62=84

 876 23+41=64 22+63=85

 877 23+42=65 22+64=86

 878 23+43=66 22+65=87

 879 23+44=67 22+66=88

 880 23+46=69 22=11+11

 881 23+49=72 22=22=22

 882 23+51=74 22=6+8+8

 883 23+52=75 22=7+7+8

 884 23+53=76 22=7+8+7

 885 23+54=77 22=8+6+8

 886 23+56=79 22=8+7+7

 887 23+69=92 22=8+8+6

 888 23+71=94 23+11=34

 889 23+72=95 23+12=35

 890 23+73=96 23+13=36

 891 23+74=97 23+14=37

 892 23+76=99 23+15=38

 893 23=11+12 23+18=41

 894 23=12+11 23+21=44

 895 23=23=23 23+22=45

 896 23=5+9+9 23+23=46

 897 23=7+7+9 23+24=47

 898 23=7+9+7 23+25=48

 899 23=9+5+9 23+28=51

 900 23=9+7+7 23+31=54

 901 23=9+9+5 23+32=55

 902 24+11=35 23+33=56

 903 24+12=36 23+34=57

 904 24+13=37 23+35=58

 905 24+15=39 23+38=61

 906 24+17=41 23+41=64

 907 24+19=43 23+42=65

 908 24+21=45 23+43=66

 909 24+22=46 23+44=67

 910 24+23=47 23+45=68

 911 24+25=49 23+48=71

 912 24+27=51 23+51=74

 913 24+29=53 23+52=75

 914 24+31=55 23+53=76

 915 24+32=56 23+54=77

 916 24+33=57 23+55=78

 917 24+35=59 23+58=81

 918 24+37=61 23+61=84

 919 24+39=63 23+62=85

 920 24+41=65 23+63=86

 921 24+42=66 23+64=87

 922 24+43=67 23+65=88

 923 24+45=69 23=11+12

 924 24+47=71 23=12+11

 925 24+49=73 23=23=23

 926 24+51=75 23=7+8+8

 927 24+52=76 23=8+7+8

 928 24+53=77 23=8+8+7

 929 24+55=79 24+11=35

 930 24+67=91 24+12=36

 931 24+69=93 24+13=37

 932 24+71=95 24+14=38

 933 24+72=96 24+17=41

 934 24+73=97 24+18=42

 935 24+75=99 24+21=45

 936 24=11+13 24+22=46

 937 24=12+12 24+23=47

 938 24=13+11 24+24=48

 939 24=24=24 24+27=51

 940 24=6+9+9 24+28=52

 941 24=9+6+9 24+31=55

 942 24=9+9+6 24+32=56

 943 25+11=36 24+33=57

 944 25+12=37 24+34=58

 945 25+14=39 24+37=61

 946 25+16=41 24+38=62

 947 25+17=42 24+41=65

 948 25+19=44 24+42=66

 949 25+21=46 24+43=67

 950 25+22=47 24+44=68

 951 25+24=49 24+47=71

 952 25+26=51 24+48=72

 953 25+27=52 24+51=75

 954 25+29=54 24+52=76

 955 25+31=56 24+53=77

 956 25+32=57 24+54=78

 957 25+34=59 24+57=81

 958 25+36=61 24+58=82

 959 25+37=62 24+61=85

 960 25+39=64 24+62=86

 961 25+41=66 24+63=87

 962 25+42=67 24+64=88

 963 25+44=69 24=11+13

 964 25+46=71 24=12+12

 965 25+47=72 24=13+11

 966 25+49=74 24=24=24

 967 25+51=76 24=8+8+8

 968 25+52=77 25+11=36

 969 25+54=79 25+12=37

 970 25+66=91 25+13=38

 971 25+67=92 25+16=41

 972 25+69=94 25+17=42

 973 25+71=96 25+18=43

 974 25+72=97 25+21=46

 975 25+74=99 25+22=47

 976 25=11+14 25+23=48

 977 25=12+13 25+26=51

 978 25=13+12 25+27=52

 979 25=14+11 25+28=53

 980 25=25=25 25+31=56

 981 25=7+9+9 25+32=57

 982 25=9+7+9 25+33=58

 983 25=9+9+7 25+36=61

 984 26+11=37 25+37=62

 985 26+13=39 25+38=63

 986 26+15=41 25+41=66

 987 26+16=42 25+42=67

 988 26+17=43 25+43=68

 989 26+19=45 25+46=71

 990 26+21=47 25+47=72

 991 26+23=49 25+48=73

 992 26+25=51 25+51=76

 993 26+26=52 25+52=77

 994 26+27=53 25+53=78

 995 26+29=55 25+56=81

 996 26+31=57 25+57=82

 997 26+33=59 25+58=83

 998 26+35=61 25+61=86

 999 26+36=62 25+62=87

1000 26+37=63 25+63=88

1001 26+39=65 25=11+14

1002 26+41=67 25=12+13

1003 26+43=69 25=13+12

1004 26+45=71 25=14+11

1005 26+46=72 25=25=25

1006 26+47=73 26+11=37

1007 26+49=75 26+12=38

1008 26+51=77 26+15=41

1009 26+53=79 26+16=42

1010 26+65=91 26+17=43

1011 26+66=92 26+18=44

1012 26+67=93 26+21=47

1013 26+69=95 26+22=48

1014 26+71=97 26+25=51

1015 26+73=99 26+26=52

1016 26=11+15 26+27=53

1017 26=12+14 26+28=54

1018 26=13+13 26+31=57

1019 26=14+12 26+32=58

1020 26=15+11 26+35=61

1021 26=26=26 26+36=62

1022 27+12=39 26+37=63

1023 27+14=41 26+38=64

1024 27+15=42 26+41=67

1025 27+16=43 26+42=68

1026 27+17=44 26+45=71

1027 27+19=46 26+46=72

1028 27+22=49 26+47=73

1029 27+24=51 26+48=74

1030 27+25=52 26+51=77

1031 27+26=53 26+52=78

1032 27+27=54 26+55=81

1033 27+29=56 26+56=82

1034 27+32=59 26+57=83

1035 27+34=61 26+58=84

1036 27+35=62 26+61=87

1037 27+36=63 26+62=88

1038 27+37=64 26=11+15

1039 27+39=66 26=12+14

1040 27+42=69 26=13+13

1041 27+44=71 26=14+12

1042 27+45=72 26=15+11

1043 27+46=73 26=26=26

1044 27+47=74 27+11=38

1045 27+49=76 27+14=41

1046 27+52=79 27+15=42

1047 27+64=91 27+16=43

1048 27+65=92 27+17=44

1049 27+66=93 27+18=45

1050 27+67=94 27+21=48

1051 27+69=96 27+24=51

1052 27+72=99 27+25=52

1053 27=11+16 27+26=53

1054 27=12+15 27+27=54

1055 27=13+14 27+28=55

1056 27=14+13 27+31=58

1057 27=15+12 27+34=61

1058 27=16+11 27+35=62

1059 27=27=27 27+36=63

1060 27=9+9+9 27+37=64

1061 29+12=41 27+38=65

1062 29+13=42 27+41=68

1063 29+14=43 27+44=71

1064 29+15=44 27+45=72

1065 29+16=45 27+46=73

1066 29+17=46 27+47=74

1067 29+22=51 27+48=75

1068 29+23=52 27+51=78

1069 29+24=53 27+54=81

1070 29+25=54 27+55=82

1071 29+26=55 27+56=83

1072 29+27=56 27+57=84

1073 29+32=61 27+58=85

1074 29+33=62 27+61=88

1075 29+34=63 27=11+16

1076 29+35=64 27=12+15

1077 29+36=65 27=13+14

1078 29+37=66 27=14+13

1079 29+42=71 27=15+12

1080 29+43=72 27=16+11

1081 29+44=73 27=27=27

1082 29+45=74 28+13=41

1083 29+46=75 28+14=42

1084 29+47=76 28+15=43

1085 29+62=91 28+16=44

1086 29+63=92 28+17=45

1087 29+64=93 28+18=46

1088 29+65=94 28+23=51

1089 29+66=95 28+24=52

1090 29+67=96 28+25=53

1091 29=12+17 28+26=54

1092 29=13+16 28+27=55

1093 29=14+15 28+28=56

1094 29=15+14 28+33=61

1095 29=16+13 28+34=62

1096 29=17+12 28+35=63

1097 29=29=29 28+36=64

1098 3+1+7=11 28+37=65

1099 3+1+9=13 28+38=66

1100 3+11=5+9 28+43=71

1101 3+11=7+7 28+44=72

1102 3+11=9+5 28+45=73

1103 3+12=6+9 28+46=74

1104 3+12=9+6 28+47=75

1105 3+13=7+9 28+48=76

1106 3+13=9+7 28+53=81

1107 3+15=9+9 28+54=82

1108 3+2+6=11 28+55=83

1109 3+2+7=12 28+56=84

1110 3+2+9=14 28+57=85

1111 3+3+5=11 28+58=86

1112 3+3+6=12 28=11+17

1113 3+3+7=13 28=12+16

1114 3+3+9=15 28=13+15

1115 3+4+4=11 28=14+14

1116 3+4+5=12 28=15+13

1117 3+4+6=13 28=16+12

1118 3+4+7=14 28=17+11

1119 3+4+9=16 28=28=28

1120 3+5+3=11 3+1+7=11

1121 3+5+4=12 3+1+8=12

1122 3+5+5=13 3+11=6+8

1123 3+5+6=14 3+11=7+7

1124 3+5+7=15 3+11=8+6

1125 3+5+9=17 3+12=7+8

1126 3+6+2=11 3+12=8+7

1127 3+6+3=12 3+13=8+8

1128 3+6+4=13 3+2+6=11

1129 3+6+5=14 3+2+7=12

1130 3+6+6=15 3+2+8=13

1131 3+6+7=16 3+3+5=11

1132 3+7+1=11 3+3+6=12

1133 3+7+2=12 3+3+7=13

1134 3+7+3=13 3+3+8=14

1135 3+7+4=14 3+4+4=11

1136 3+7+5=15 3+4+5=12

1137 3+7+6=16 3+4+6=13

1138 3+7+7=17 3+4+7=14

1139 3+7+9=19 3+4+8=15

1140 3+9+1=13 3+5+3=11

1141 3+9+2=14 3+5+4=12

1142 3+9+3=15 3+5+5=13

1143 3+9+4=16 3+5+6=14

1144 3+9+5=17 3+5+7=15

1145 3+9+7=19 3+5+8=16

1146 3+9+9=21 3+6+2=11

1147 3+9=1+11 3+6+3=12

1148 3+9=11+1 3+6+4=13

1149 31+11=42 3+6+5=14

1150 31+12=43 3+6+6=15

1151 31+13=44 3+6+7=16

1152 31+14=45 3+6+8=17

1153 31+15=46 3+7+1=11

1154 31+16=47 3+7+2=12

1155 31+21=52 3+7+3=13

1156 31+22=53 3+7+4=14

1157 31+23=54 3+7+5=15

1158 31+24=55 3+7+6=16

1159 31+25=56 3+7+7=17

1160 31+26=57 3+7+8=18

1161 31+31=62 3+8+1=12

1162 31+32=63 3+8+2=13

1163 31+33=64 3+8+3=14

1164 31+34=65 3+8+4=15

1165 31+35=66 3+8+5=16

1166 31+36=67 3+8+6=17

1167 31+41=72 3+8+7=18

1168 31+42=73 31+11=42

1169 31+43=74 31+12=43

1170 31+44=75 31+13=44

1171 31+45=76 31+14=45

1172 31+46=77 31+15=46

1173 31+61=92 31+16=47

1174 31+62=93 31+17=48

1175 31+63=94 31+21=52

1176 31+64=95 31+22=53

1177 31+65=96 31+23=54

1178 31+66=97 31+24=55

1179 31=12+19 31+25=56

1180 31=14+17 31+26=57

1181 31=15+16 31+27=58

1182 31=16+15 31+31=62

1183 31=17+14 31+32=63

1184 31=19+12 31+33=64

1185 31=31=31 31+34=65

1186 32+11=43 31+35=66

1187 32+12=44 31+36=67

1188 32+13=45 31+37=68

1189 32+14=46 31+41=72

1190 32+15=47 31+42=73

1191 32+17=49 31+43=74

1192 32+19=51 31+44=75

1193 32+21=53 31+45=76

1194 32+22=54 31+46=77

1195 32+23=55 31+47=78

1196 32+24=56 31+51=82

1197 32+25=57 31+52=83

1198 32+27=59 31+53=84

1199 32+29=61 31+54=85

1200 32+31=63 31+55=86

1201 32+32=64 31+56=87

1202 32+33=65 31+57=88

1203 32+34=66 31=13+18

1204 32+35=67 31=14+17

1205 32+37=69 31=15+16

1206 32+39=71 31=16+15

1207 32+41=73 31=17+14

1208 32+42=74 31=18+13

1209 32+43=75 31=31=31

1210 32+44=76 32+11=43

1211 32+45=77 32+12=44

1212 32+47=79 32+13=45

1213 32+59=91 32+14=46

1214 32+61=93 32+15=47

1215 32+62=94 32+16=48

1216 32+63=95 32+21=53

1217 32+64=96 32+22=54

1218 32+65=97 32+23=55

1219 32+67=99 32+24=56

1220 32=11+21 32+25=57

1221 32=13+19 32+26=58

1222 32=15+17 32+31=63

1223 32=16+16 32+32=64

1224 32=17+15 32+33=65

1225 32=19+13 32+34=66

1226 32=21+11 32+35=67

1227 32=32=32 32+36=68

1228 33+11=44 32+41=73

1229 33+12=45 32+42=74

1230 33+13=46 32+43=75

1231 33+14=47 32+44=76

1232 33+16=49 32+45=77

1233 33+19=52 32+46=78

1234 33+21=54 32+51=83

1235 33+22=55 32+52=84

1236 33+23=56 32+53=85

1237 33+24=57 32+54=86

1238 33+26=59 32+55=87

1239 33+29=62 32+56=88

1240 33+31=64 32=11+21

1241 33+32=65 32=14+18

1242 33+33=66 32=15+17

1243 33+34=67 32=16+16

1244 33+36=69 32=17+15

1245 33+39=72 32=18+14

1246 33+41=74 32=21+11

1247 33+42=75 32=32=32

1248 33+43=76 33+11=44

1249 33+44=77 33+12=45

1250 33+46=79 33+13=46

1251 33+59=92 33+14=47

1252 33+61=94 33+15=48

1253 33+62=95 33+18=51

1254 33+63=96 33+21=54

1255 33+64=97 33+22=55

1256 33+66=99 33+23=56

1257 33=11+22 33+24=57

1258 33=12+21 33+25=58

1259 33=14+19 33+28=61

1260 33=16+17 33+31=64

1261 33=17+16 33+32=65

1262 33=19+14 33+33=66

1263 33=21+12 33+34=67

1264 33=22+11 33+35=68

1265 33=33=33 33+38=71

1266 34+11=45 33+41=74

1267 34+12=46 33+42=75

1268 34+13=47 33+43=76

1269 34+15=49 33+44=77

1270 34+17=51 33+45=78

1271 34+19=53 33+48=81

1272 34+21=55 33+51=84

1273 34+22=56 33+52=85

1274 34+23=57 33+53=86

1275 34+25=59 33+54=87

1276 34+27=61 33+55=88

1277 34+29=63 33=11+22

1278 34+31=65 33=12+21

1279 34+32=66 33=15+18

1280 34+33=67 33=16+17

1281 34+35=69 33=17+16

1282 34+37=71 33=18+15

1283 34+39=73 33=21+12

1284 34+41=75 33=22+11

1285 34+42=76 33=33=33

1286 34+43=77 34+11=45

1287 34+45=79 34+12=46

1288 34+57=91 34+13=47

1289 34+59=93 34+14=48

1290 34+61=95 34+17=51

1291 34+62=96 34+18=52

1292 34+63=97 34+21=55

1293 34+65=99 34+22=56

1294 34=11+23 34+23=57

1295 34=12+22 34+24=58

1296 34=13+21 34+27=61

1297 34=15+19 34+28=62

1298 34=17+17 34+31=65

1299 34=19+15 34+32=66

1300 34=21+13 34+33=67

1301 34=22+12 34+34=68

1302 34=23+11 34+37=71

1303 34=34=34 34+38=72

1304 35+11=46 34+41=75

1305 35+12=47 34+42=76

1306 35+14=49 34+43=77

1307 35+16=51 34+44=78

1308 35+17=52 34+47=81

1309 35+19=54 34+48=82

1310 35+21=56 34+51=85

1311 35+22=57 34+52=86

1312 35+24=59 34+53=87

1313 35+26=61 34+54=88

1314 35+27=62 34=11+23

1315 35+29=64 34=12+22

1316 35+31=66 34=13+21

1317 35+32=67 34=16+18

1318 35+34=69 34=17+17

1319 35+36=71 34=18+16

1320 35+37=72 34=21+13

1321 35+39=74 34=22+12

1322 35+41=76 34=23+11

1323 35+42=77 34=34=34

1324 35+44=79 35+11=46

1325 35+56=91 35+12=47

1326 35+57=92 35+13=48

1327 35+59=94 35+16=51

1328 35+61=96 35+17=52

1329 35+62=97 35+18=53

1330 35+64=99 35+21=56

1331 35=11+24 35+22=57

1332 35=12+23 35+23=58

1333 35=13+22 35+26=61

1334 35=14+21 35+27=62

1335 35=16+19 35+28=63

1336 35=19+16 35+31=66

1337 35=21+14 35+32=67

1338 35=22+13 35+33=68

1339 35=23+12 35+36=71

1340 35=24+11 35+37=72

1341 35=35=35 35+38=73

1342 36+11=47 35+41=76

1343 36+13=49 35+42=77

1344 36+15=51 35+43=78

1345 36+16=52 35+46=81

1346 36+17=53 35+47=82

1347 36+19=55 35+48=83

1348 36+21=57 35+51=86

1349 36+23=59 35+52=87

1350 36+25=61 35+53=88

1351 36+26=62 35=11+24

1352 36+27=63 35=12+23

1353 36+29=65 35=13+22

1354 36+31=67 35=14+21

1355 36+33=69 35=17+18

1356 36+35=71 35=18+17

1357 36+36=72 35=21+14

1358 36+37=73 35=22+13

1359 36+39=75 35=23+12

1360 36+41=77 35=24+11

1361 36+43=79 35=35=35

1362 36+55=91 36+11=47

1363 36+56=92 36+12=48

1364 36+57=93 36+15=51

1365 36+59=95 36+16=52

1366 36+61=97 36+17=53

1367 36+63=99 36+18=54

1368 36=11+25 36+21=57

1369 36=12+24 36+22=58

1370 36=13+23 36+25=61

1371 36=14+22 36+26=62

1372 36=15+21 36+27=63

1373 36=17+19 36+28=64

1374 36=19+17 36+31=67

1375 36=21+15 36+32=68

1376 36=22+14 36+35=71

1377 36=23+13 36+36=72

1378 36=24+12 36+37=73

1379 36=25+11 36+38=74

1380 36=36=36 36+41=77

1381 37+12=49 36+42=78

1382 37+14=51 36+45=81

1383 37+15=52 36+46=82

1384 37+16=53 36+47=83

1385 37+17=54 36+48=84

1386 37+19=56 36+51=87

1387 37+22=59 36+52=88

1388 37+24=61 36=11+25

1389 37+25=62 36=12+24

1390 37+26=63 36=13+23

1391 37+27=64 36=14+22

1392 37+29=66 36=15+21

1393 37+32=69 36=18+18

1394 37+34=71 36=21+15

1395 37+35=72 36=22+14

1396 37+36=73 36=23+13

1397 37+37=74 36=24+12

1398 37+39=76 36=25+11

1399 37+42=79 36=36=36

1400 37+54=91 37+11=48

1401 37+55=92 37+14=51

1402 37+56=93 37+15=52

1403 37+57=94 37+16=53

1404 37+59=96 37+17=54

1405 37+62=99 37+18=55

1406 37=11+26 37+21=58

1407 37=12+25 37+24=61

1408 37=13+24 37+25=62

1409 37=14+23 37+26=63

1410 37=15+22 37+27=64

1411 37=16+21 37+28=65

1412 37=21+16 37+31=68

1413 37=22+15 37+34=71

1414 37=23+14 37+35=72

1415 37=24+13 37+36=73

1416 37=25+12 37+37=74

1417 37=26+11 37+38=75

1418 37=37=37 37+41=78

1419 39+12=51 37+44=81

1420 39+13=52 37+45=82

1421 39+14=53 37+46=83

1422 39+15=54 37+47=84

1423 39+16=55 37+48=85

1424 39+17=56 37+51=88

1425 39+22=61 37=11+26

1426 39+23=62 37=12+25

1427 39+24=63 37=13+24

1428 39+25=64 37=14+23

1429 39+26=65 37=15+22

1430 39+27=66 37=16+21

1431 39+32=71 37=21+16

1432 39+33=72 37=22+15

1433 39+34=73 37=23+14

1434 39+35=74 37=24+13

1435 39+36=75 37=25+12

1436 39+37=76 37=26+11

1437 39+52=91 37=37=37

1438 39+53=92 38+13=51

1439 39+54=93 38+14=52

1440 39+55=94 38+15=53

1441 39+56=95 38+16=54

1442 39+57=96 38+17=55

1443 39=12+27 38+18=56

1444 39=13+26 38+23=61

1445 39=14+25 38+24=62

1446 39=15+24 38+25=63

1447 39=16+23 38+26=64

1448 39=17+22 38+27=65

1449 39=22+17 38+28=66

1450 39=23+16 38+33=71

1451 39=24+15 38+34=72

1452 39=25+14 38+35=73

1453 39=26+13 38+36=74

1454 39=27+12 38+37=75

1455 39=39=39 38+38=76

1456 4+1+6=11 38+43=81

1457 4+1+7=12 38+44=82

1458 4+1+9=14 38+45=83

1459 4+11=6+9 38+46=84

1460 4+11=9+6 38+47=85

1461 4+12=7+9 38+48=86

1462 4+12=9+7 38=11+27

1463 4+14=9+9 38=12+26

1464 4+2+5=11 38=13+25

1465 4+2+6=12 38=14+24

1466 4+2+7=13 38=15+23

1467 4+2+9=15 38=16+22

1468 4+3+4=11 38=17+21

1469 4+3+5=12 38=21+17

1470 4+3+6=13 38=22+16

1471 4+3+7=14 38=23+15

1472 4+3+9=16 38=24+14

1473 4+4+3=11 38=25+13

1474 4+4+4=12 38=26+12

1475 4+4+5=13 38=27+11

1476 4+4+6=14 38=38=38

1477 4+4+7=15 4+1+6=11

1478 4+4+9=17 4+1+7=12

1479 4+5+2=11 4+1+8=13

1480 4+5+3=12 4+11=7+8

1481 4+5+4=13 4+11=8+7

1482 4+5+5=14 4+12=8+8

1483 4+5+6=15 4+2+5=11

1484 4+5+7=16 4+2+6=12

1485 4+6+1=11 4+2+7=13

1486 4+6+2=12 4+2+8=14

1487 4+6+3=13 4+3+4=11

1488 4+6+4=14 4+3+5=12

1489 4+6+5=15 4+3+6=13

1490 4+6+6=16 4+3+7=14

1491 4+6+7=17 4+3+8=15

1492 4+6+9=19 4+4+3=11

1493 4+7+1=12 4+4+4=12

1494 4+7+2=13 4+4+5=13

1495 4+7+3=14 4+4+6=14

1496 4+7+4=15 4+4+7=15

1497 4+7+5=16 4+4+8=16

1498 4+7+6=17 4+5+2=11

1499 4+9+1=14 4+5+3=12

1500 4+9+2=15 4+5+4=13

1501 4+9+3=16 4+5+5=14

1502 4+9+4=17 4+5+6=15

1503 4+9+6=19 4+5+7=16

1504 4+9+9=22 4+5+8=17

1505 4+9=1+12 4+6+1=11

1506 4+9=11+2 4+6+2=12

1507 4+9=12+1 4+6+3=13

1508 4+9=2+11 4+6+4=14

1509 41+11=52 4+6+5=15

1510 41+12=53 4+6+6=16

1511 41+13=54 4+6+7=17

1512 41+14=55 4+6+8=18

1513 41+15=56 4+7+1=12

1514 41+16=57 4+7+2=13

1515 41+21=62 4+7+3=14

1516 41+22=63 4+7+4=15

1517 41+23=64 4+7+5=16

1518 41+24=65 4+7+6=17

1519 41+25=66 4+7+7=18

1520 41+26=67 4+8+1=13

1521 41+31=72 4+8+2=14

1522 41+32=73 4+8+3=15

1523 41+33=74 4+8+4=16

1524 41+34=75 4+8+5=17

1525 41+35=76 4+8+6=18

1526 41+36=77 4+8=1+11

1527 41+51=92 4+8=11+1

1528 41+52=93 41+11=52

1529 41+53=94 41+12=53

1530 41+54=95 41+13=54

1531 41+55=96 41+14=55

1532 41+56=97 41+15=56

1533 41=12+29 41+16=57

1534 41=14+27 41+17=58

1535 41=15+26 41+21=62

1536 41=16+25 41+22=63

1537 41=17+24 41+23=64

1538 41=19+22 41+24=65

1539 41=22+19 41+25=66

1540 41=24+17 41+26=67

1541 41=25+16 41+27=68

1542 41=26+15 41+31=72

1543 41=27+14 41+32=73

1544 41=29+12 41+33=74

1545 41=41=41 41+34=75

1546 42+11=53 41+35=76

1547 42+12=54 41+36=77

1548 42+13=55 41+37=78

1549 42+14=56 41+41=82

1550 42+15=57 41+42=83

1551 42+17=59 41+43=84

1552 42+19=61 41+44=85

1553 42+21=63 41+45=86

1554 42+22=64 41+46=87

1555 42+23=65 41+47=88

1556 42+24=66 41=13+28

1557 42+25=67 41=14+27

1558 42+27=69 41=15+26

1559 42+29=71 41=16+25

1560 42+31=73 41=17+24

1561 42+32=74 41=18+23

1562 42+33=75 41=23+18

1563 42+34=76 41=24+17

1564 42+35=77 41=25+16

1565 42+37=79 41=26+15

1566 42+49=91 41=27+14

1567 42+51=93 41=28+13

1568 42+52=94 41=41=41

1569 42+53=95 42+11=53

1570 42+54=96 42+12=54

1571 42+55=97 42+13=55

1572 42+57=99 42+14=56

1573 42=11+31 42+15=57

1574 42=13+29 42+16=58

1575 42=15+27 42+21=63

1576 42=16+26 42+22=64

1577 42=17+25 42+23=65

1578 42=19+23 42+24=66

1579 42=21+21 42+25=67

1580 42=23+19 42+26=68

1581 42=25+17 42+31=73

1582 42=26+16 42+32=74

1583 42=27+15 42+33=75

1584 42=29+13 42+34=76

1585 42=31+11 42+35=77

1586 42=42=42 42+36=78

1587 43+11=54 42+41=83

1588 43+12=55 42+42=84

1589 43+13=56 42+43=85

1590 43+14=57 42+44=86

1591 43+16=59 42+45=87

1592 43+19=62 42+46=88

1593 43+21=64 42=11+31

1594 43+22=65 42=14+28

1595 43+23=66 42=15+27

1596 43+24=67 42=16+26

1597 43+26=69 42=17+25

1598 43+29=72 42=18+24

1599 43+31=74 42=21+21

1600 43+32=75 42=24+18

1601 43+33=76 42=25+17

1602 43+34=77 42=26+16

1603 43+36=79 42=27+15

1604 43+49=92 42=28+14

1605 43+51=94 42=31+11

1606 43+52=95 42=42=42

1607 43+53=96 43+11=54

1608 43+54=97 43+12=55

1609 43+56=99 43+13=56

1610 43=11+32 43+14=57

1611 43=12+31 43+15=58

1612 43=14+29 43+18=61

1613 43=16+27 43+21=64

1614 43=17+26 43+22=65

1615 43=19+24 43+23=66

1616 43=21+22 43+24=67

1617 43=22+21 43+25=68

1618 43=24+19 43+28=71

1619 43=26+17 43+31=74

1620 43=27+16 43+32=75

1621 43=29+14 43+33=76

1622 43=31+12 43+34=77

1623 43=32+11 43+35=78

1624 43=43=43 43+38=81

1625 44+11=55 43+41=84

1626 44+12=56 43+42=85

1627 44+13=57 43+43=86

1628 44+15=59 43+44=87

1629 44+17=61 43+45=88

1630 44+19=63 43=11+32

1631 44+21=65 43=12+31

1632 44+22=66 43=15+28

1633 44+23=67 43=16+27

1634 44+25=69 43=17+26

1635 44+27=71 43=18+25

1636 44+29=73 43=21+22

1637 44+31=75 43=22+21

1638 44+32=76 43=25+18

1639 44+33=77 43=26+17

1640 44+35=79 43=27+16

1641 44+47=91 43=28+15

1642 44+49=93 43=31+12

1643 44+51=95 43=32+11

1644 44+52=96 43=43=43

1645 44+53=97 44+11=55

1646 44+55=99 44+12=56

1647 44=11+33 44+13=57

1648 44=12+32 44+14=58

1649 44=13+31 44+17=61

1650 44=15+29 44+18=62

1651 44=17+27 44+21=65

1652 44=19+25 44+22=66

1653 44=21+23 44+23=67

1654 44=22+22 44+24=68

1655 44=23+21 44+27=71

1656 44=25+19 44+28=72

1657 44=27+17 44+31=75

1658 44=29+15 44+32=76

1659 44=31+13 44+33=77

1660 44=32+12 44+34=78

1661 44=33+11 44+37=81

1662 44=44=44 44+38=82

1663 45+11=56 44+41=85

1664 45+12=57 44+42=86

1665 45+14=59 44+43=87

1666 45+16=61 44+44=88

1667 45+17=62 44=11+33

1668 45+19=64 44=12+32

1669 45+21=66 44=13+31

1670 45+22=67 44=16+28

1671 45+24=69 44=17+27

1672 45+26=71 44=18+26

1673 45+27=72 44=21+23

1674 45+29=74 44=22+22

1675 45+31=76 44=23+21

1676 45+32=77 44=26+18

1677 45+34=79 44=27+17

1678 45+46=91 44=28+16

1679 45+47=92 44=31+13

1680 45+49=94 44=32+12

1681 45+51=96 44=33+11

1682 45+52=97 44=44=44

1683 45+54=99 45+11=56

1684 45=11+34 45+12=57

1685 45=12+33 45+13=58

1686 45=13+32 45+16=61

1687 45=14+31 45+17=62

1688 45=16+29 45+18=63

1689 45=19+26 45+21=66

1690 45=21+24 45+22=67

1691 45=22+23 45+23=68

1692 45=23+22 45+26=71

1693 45=24+21 45+27=72

1694 45=26+19 45+28=73

1695 45=29+16 45+31=76

1696 45=31+14 45+32=77

1697 45=32+13 45+33=78

1698 45=33+12 45+36=81

1699 45=34+11 45+37=82

1700 45=45=45 45+38=83

1701 46+11=57 45+41=86

1702 46+13=59 45+42=87

1703 46+15=61 45+43=88

1704 46+16=62 45=11+34

1705 46+17=63 45=12+33

1706 46+19=65 45=13+32

1707 46+21=67 45=14+31

1708 46+23=69 45=17+28

1709 46+25=71 45=18+27

1710 46+26=72 45=21+24

1711 46+27=73 45=22+23

1712 46+29=75 45=23+22

1713 46+31=77 45=24+21

1714 46+33=79 45=27+18

1715 46+45=91 45=28+17

1716 46+46=92 45=31+14

1717 46+47=93 45=32+13

1718 46+49=95 45=33+12

1719 46+51=97 45=34+11

1720 46+53=99 45=45=45

1721 46=11+35 46+11=57

1722 46=12+34 46+12=58

1723 46=13+33 46+15=61

1724 46=14+32 46+16=62

1725 46=15+31 46+17=63

1726 46=17+29 46+18=64

1727 46=19+27 46+21=67

1728 46=21+25 46+22=68

1729 46=22+24 46+25=71

1730 46=23+23 46+26=72

1731 46=24+22 46+27=73

1732 46=25+21 46+28=74

1733 46=27+19 46+31=77

1734 46=29+17 46+32=78

1735 46=31+15 46+35=81

1736 46=32+14 46+36=82

1737 46=33+13 46+37=83

1738 46=34+12 46+38=84

1739 46=35+11 46+41=87

1740 46=46=46 46+42=88

1741 47+12=59 46=11+35

1742 47+14=61 46=12+34

1743 47+15=62 46=13+33

1744 47+16=63 46=14+32

1745 47+17=64 46=15+31

1746 47+19=66 46=18+28

1747 47+22=69 46=21+25

1748 47+24=71 46=22+24

1749 47+25=72 46=23+23

1750 47+26=73 46=24+22

1751 47+27=74 46=25+21

1752 47+29=76 46=28+18

1753 47+32=79 46=31+15

1754 47+44=91 46=32+14

1755 47+45=92 46=33+13

1756 47+46=93 46=34+12

1757 47+47=94 46=35+11

1758 47+49=96 46=46=46

1759 47+52=99 47+11=58

1760 47=11+36 47+14=61

1761 47=12+35 47+15=62

1762 47=13+34 47+16=63

1763 47=14+33 47+17=64

1764 47=15+32 47+18=65

1765 47=16+31 47+21=68

1766 47=21+26 47+24=71

1767 47=22+25 47+25=72

1768 47=23+24 47+26=73

1769 47=24+23 47+27=74

1770 47=25+22 47+28=75

1771 47=26+21 47+31=78

1772 47=31+16 47+34=81

1773 47=32+15 47+35=82

1774 47=33+14 47+36=83

1775 47=34+13 47+37=84

1776 47=35+12 47+38=85

1777 47=36+11 47+41=88

1778 47=47=47 47=11+36

1779 49+12=61 47=12+35

1780 49+13=62 47=13+34

1781 49+14=63 47=14+33

1782 49+15=64 47=15+32

1783 49+16=65 47=16+31

1784 49+17=66 47=21+26

1785 49+22=71 47=22+25

1786 49+23=72 47=23+24

1787 49+24=73 47=24+23

1788 49+25=74 47=25+22

1789 49+26=75 47=26+21

1790 49+27=76 47=31+16

1791 49+42=91 47=32+15

1792 49+43=92 47=33+14

1793 49+44=93 47=34+13

1794 49+45=94 47=35+12

1795 49+46=95 47=36+11

1796 49+47=96 47=47=47

1797 49=12+37 48+13=61

1798 49=13+36 48+14=62

1799 49=14+35 48+15=63

1800 49=15+34 48+16=64

1801 49=16+33 48+17=65

1802 49=17+32 48+18=66

1803 49=22+27 48+23=71

1804 49=23+26 48+24=72

1805 49=24+25 48+25=73

1806 49=25+24 48+26=74

1807 49=26+23 48+27=75

1808 49=27+22 48+28=76

1809 49=32+17 48+33=81

1810 49=33+16 48+34=82

1811 49=34+15 48+35=83

1812 49=35+14 48+36=84

1813 49=36+13 48+37=85

1814 49=37+12 48+38=86

1815 49=49=49 48=11+37

1816 5+1+5=11 48=12+36

1817 5+1+6=12 48=13+35

1818 5+1+7=13 48=14+34

1819 5+1+9=15 48=15+33

1820 5+11=7+9 48=16+32

1821 5+11=9+7 48=17+31

1822 5+13=9+9 48=21+27

1823 5+2+4=11 48=22+26

1824 5+2+5=12 48=23+25

1825 5+2+6=13 48=24+24

1826 5+2+7=14 48=25+23

1827 5+2+9=16 48=26+22

1828 5+3+3=11 48=27+21

1829 5+3+4=12 48=31+17

1830 5+3+5=13 48=32+16

1831 5+3+6=14 48=33+15

1832 5+3+7=15 48=34+14

1833 5+3+9=17 48=35+13

1834 5+4+2=11 48=36+12

1835 5+4+3=12 48=37+11

1836 5+4+4=13 48=48=48

1837 5+4+5=14 5+1+5=11

1838 5+4+6=15 5+1+6=12

1839 5+4+7=16 5+1+7=13

1840 5+5+1=11 5+1+8=14

1841 5+5+2=12 5+11=8+8

1842 5+5+3=13 5+2+4=11

1843 5+5+4=14 5+2+5=12

1844 5+5+5=15 5+2+6=13

1845 5+5+6=16 5+2+7=14

1846 5+5+7=17 5+2+8=15

1847 5+5+9=19 5+3+3=11

1848 5+6+1=12 5+3+4=12

1849 5+6+2=13 5+3+5=13

1850 5+6+3=14 5+3+6=14

1851 5+6+4=15 5+3+7=15

1852 5+6+5=16 5+3+8=16

1853 5+6+6=17 5+4+2=11

1854 5+7+1=13 5+4+3=12

1855 5+7+2=14 5+4+4=13

1856 5+7+3=15 5+4+5=14

1857 5+7+4=16 5+4+6=15

1858 5+7+5=17 5+4+7=16

1859 5+7+7=19 5+4+8=17

1860 5+7+9=21 5+5+1=11

1861 5+7=1+11 5+5+2=12

1862 5+7=11+1 5+5+3=13

1863 5+9+1=15 5+5+4=14

1864 5+9+2=16 5+5+5=15

1865 5+9+3=17 5+5+6=16

1866 5+9+5=19 5+5+7=17

1867 5+9+7=21 5+5+8=18

1868 5+9+9=23 5+6+1=12

1869 5+9=1+13 5+6+2=13

1870 5+9=11+3 5+6+3=14

1871 5+9=12+2 5+6+4=15

1872 5+9=13+1 5+6+5=16

1873 5+9=2+12 5+6+6=17

1874 5+9=3+11 5+6+7=18

1875 51+11=62 5+7+1=13

1876 51+12=63 5+7+2=14

1877 51+13=64 5+7+3=15

1878 51+14=65 5+7+4=16

1879 51+15=66 5+7+5=17

1880 51+16=67 5+7+6=18

1881 51+21=72 5+7=1+11

1882 51+22=73 5+7=11+1

1883 51+23=74 5+8+1=14

1884 51+24=75 5+8+2=15

1885 51+25=76 5+8+3=16

1886 51+26=77 5+8+4=17

1887 51+41=92 5+8+5=18

1888 51+42=93 5+8+8=21

1889 51+43=94 5+8=1+12

1890 51+44=95 5+8=11+2

1891 51+45=96 5+8=12+1

1892 51+46=97 5+8=2+11

1893 51=12+39 51+11=62

1894 51=14+37 51+12=63

1895 51=15+36 51+13=64

1896 51=16+35 51+14=65

1897 51=17+34 51+15=66

1898 51=19+32 51+16=67

1899 51=22+29 51+17=68

1900 51=24+27 51+21=72

1901 51=25+26 51+22=73

1902 51=26+25 51+23=74

1903 51=27+24 51+24=75

1904 51=29+22 51+25=76

1905 51=32+19 51+26=77

1906 51=34+17 51+27=78

1907 51=35+16 51+31=82

1908 51=36+15 51+32=83

1909 51=37+14 51+33=84

1910 51=39+12 51+34=85

1911 51=51=51 51+35=86

1912 52+11=63 51+36=87

1913 52+12=64 51+37=88

1914 52+13=65 51=13+38

1915 52+14=66 51=14+37

1916 52+15=67 51=15+36

1917 52+17=69 51=16+35

1918 52+19=71 51=17+34

1919 52+21=73 51=18+33

1920 52+22=74 51=23+28

1921 52+23=75 51=24+27

1922 52+24=76 51=25+26

1923 52+25=77 51=26+25

1924 52+27=79 51=27+24

1925 52+39=91 51=28+23

1926 52+41=93 51=33+18

1927 52+42=94 51=34+17

1928 52+43=95 51=35+16

1929 52+44=96 51=36+15

1930 52+45=97 51=37+14

1931 52+47=99 51=38+13

1932 52=11+41 51=51=51

1933 52=13+39 52+11=63

1934 52=15+37 52+12=64

1935 52=16+36 52+13=65

1936 52=17+35 52+14=66

1937 52=19+33 52+15=67

1938 52=21+31 52+16=68

1939 52=23+29 52+21=73

1940 52=25+27 52+22=74

1941 52=26+26 52+23=75

1942 52=27+25 52+24=76

1943 52=29+23 52+25=77

1944 52=31+21 52+26=78

1945 52=33+19 52+31=83

1946 52=35+17 52+32=84

1947 52=36+16 52+33=85

1948 52=37+15 52+34=86

1949 52=39+13 52+35=87

1950 52=41+11 52+36=88

1951 52=52=52 52=11+41

1952 53+11=64 52=14+38

1953 53+12=65 52=15+37

1954 53+13=66 52=16+36

1955 53+14=67 52=17+35

1956 53+16=69 52=18+34

1957 53+19=72 52=21+31

1958 53+21=74 52=24+28

1959 53+22=75 52=25+27

1960 53+23=76 52=26+26

1961 53+24=77 52=27+25

1962 53+26=79 52=28+24

1963 53+39=92 52=31+21

1964 53+41=94 52=34+18

1965 53+42=95 52=35+17

1966 53+43=96 52=36+16

1967 53+44=97 52=37+15

1968 53+46=99 52=38+14

1969 53=11+42 52=41+11

1970 53=12+41 52=52=52

1971 53=14+39 53+11=64

1972 53=16+37 53+12=65

1973 53=17+36 53+13=66

1974 53=19+34 53+14=67

1975 53=21+32 53+15=68

1976 53=22+31 53+18=71

1977 53=24+29 53+21=74

1978 53=26+27 53+22=75

1979 53=27+26 53+23=76

1980 53=29+24 53+24=77

1981 53=31+22 53+25=78

1982 53=32+21 53+28=81

1983 53=34+19 53+31=84

1984 53=36+17 53+32=85

1985 53=37+16 53+33=86

1986 53=39+14 53+34=87

1987 53=41+12 53+35=88

1988 53=42+11 53=11+42

1989 53=53=53 53=12+41

1990 54+11=65 53=15+38

1991 54+12=66 53=16+37

1992 54+13=67 53=17+36

1993 54+15=69 53=18+35

1994 54+17=71 53=21+32

1995 54+19=73 53=22+31

1996 54+21=75 53=25+28

1997 54+22=76 53=26+27

1998 54+23=77 53=27+26

1999 54+25=79 53=28+25

2000 54+37=91 53=31+22

2001 54+39=93 53=32+21

2002 54+41=95 53=35+18

2003 54+42=96 53=36+17

2004 54+43=97 53=37+16

2005 54+45=99 53=38+15

2006 54=11+43 53=41+12

2007 54=12+42 53=42+11

2008 54=13+41 53=53=53

2009 54=15+39 54+11=65

2010 54=17+37 54+12=66

2011 54=19+35 54+13=67

2012 54=21+33 54+14=68

2013 54=22+32 54+17=71

2014 54=23+31 54+18=72

2015 54=25+29 54+21=75

2016 54=27+27 54+22=76

2017 54=29+25 54+23=77

2018 54=31+23 54+24=78

2019 54=32+22 54+27=81

2020 54=33+21 54+28=82

2021 54=35+19 54+31=85

2022 54=37+17 54+32=86

2023 54=39+15 54+33=87

2024 54=41+13 54+34=88

2025 54=42+12 54=11+43

2026 54=43+11 54=12+42

2027 54=54=54 54=13+41

2028 55+11=66 54=16+38

2029 55+12=67 54=17+37

2030 55+14=69 54=18+36

2031 55+16=71 54=21+33

2032 55+17=72 54=22+32

2033 55+19=74 54=23+31

2034 55+21=76 54=26+28

2035 55+22=77 54=27+27

2036 55+24=79 54=28+26

2037 55+36=91 54=31+23

2038 55+37=92 54=32+22

2039 55+39=94 54=33+21

2040 55+41=96 54=36+18

2041 55+42=97 54=37+17

2042 55+44=99 54=38+16

2043 55=11+44 54=41+13

2044 55=12+43 54=42+12

2045 55=13+42 54=43+11

2046 55=14+41 54=54=54

2047 55=16+39 55+11=66

2048 55=19+36 55+12=67

2049 55=21+34 55+13=68

2050 55=22+33 55+16=71

2051 55=23+32 55+17=72

2052 55=24+31 55+18=73

2053 55=26+29 55+21=76

2054 55=29+26 55+22=77

2055 55=31+24 55+23=78

2056 55=32+23 55+26=81

2057 55=33+22 55+27=82

2058 55=34+21 55+28=83

2059 55=36+19 55+31=86

2060 55=39+16 55+32=87

2061 55=41+14 55+33=88

2062 55=42+13 55=11+44

2063 55=43+12 55=12+43

2064 55=44+11 55=13+42

2065 55=55=55 55=14+41

2066 56+11=67 55=17+38

2067 56+13=69 55=18+37

2068 56+15=71 55=21+34

2069 56+16=72 55=22+33

2070 56+17=73 55=23+32

2071 56+19=75 55=24+31

2072 56+21=77 55=27+28

2073 56+23=79 55=28+27

2074 56+35=91 55=31+24

2075 56+36=92 55=32+23

2076 56+37=93 55=33+22

2077 56+39=95 55=34+21

2078 56+41=97 55=37+18

2079 56+43=99 55=38+17

2080 56=11+45 55=41+14

2081 56=12+44 55=42+13

2082 56=13+43 55=43+12

2083 56=14+42 55=44+11

2084 56=15+41 55=55=55

2085 56=17+39 56+11=67

2086 56=19+37 56+12=68

2087 56=21+35 56+15=71

2088 56=22+34 56+16=72

2089 56=23+33 56+17=73

2090 56=24+32 56+18=74

2091 56=25+31 56+21=77

2092 56=27+29 56+22=78

2093 56=29+27 56+25=81

2094 56=31+25 56+26=82

2095 56=32+24 56+27=83

2096 56=33+23 56+28=84

2097 56=34+22 56+31=87

2098 56=35+21 56+32=88

2099 56=37+19 56=11+45

2100 56=39+17 56=12+44

2101 56=41+15 56=13+43

2102 56=42+14 56=14+42

2103 56=43+13 56=15+41

2104 56=44+12 56=18+38

2105 56=45+11 56=21+35

2106 56=56=56 56=22+34

2107 57+12=69 56=23+33

2108 57+14=71 56=24+32

2109 57+15=72 56=25+31

2110 57+16=73 56=28+28

2111 57+17=74 56=31+25

2112 57+19=76 56=32+24

2113 57+22=79 56=33+23

2114 57+34=91 56=34+22

2115 57+35=92 56=35+21

2116 57+36=93 56=38+18

2117 57+37=94 56=41+15

2118 57+39=96 56=42+14

2119 57+42=99 56=43+13

2120 57=11+46 56=44+12

2121 57=12+45 56=45+11

2122 57=13+44 56=56=56

2123 57=14+43 57+11=68

2124 57=15+42 57+14=71

2125 57=16+41 57+15=72

2126 57=21+36 57+16=73

2127 57=22+35 57+17=74

2128 57=23+34 57+18=75

2129 57=24+33 57+21=78

2130 57=25+32 57+24=81

2131 57=26+31 57+25=82

2132 57=31+26 57+26=83

2133 57=32+25 57+27=84

2134 57=33+24 57+28=85

2135 57=34+23 57+31=88

2136 57=35+22 57=11+46

2137 57=36+21 57=12+45

2138 57=41+16 57=13+44

2139 57=42+15 57=14+43

2140 57=43+14 57=15+42

2141 57=44+13 57=16+41

2142 57=45+12 57=21+36

2143 57=46+11 57=22+35

2144 57=57=57 57=23+34

2145 59+12=71 57=24+33

2146 59+13=72 57=25+32

2147 59+14=73 57=26+31

2148 59+15=74 57=31+26

2149 59+16=75 57=32+25

2150 59+17=76 57=33+24

2151 59+32=91 57=34+23

2152 59+33=92 57=35+22

2153 59+34=93 57=36+21

2154 59+35=94 57=41+16

2155 59+36=95 57=42+15

2156 59+37=96 57=43+14

2157 59=12+47 57=44+13

2158 59=13+46 57=45+12

2159 59=14+45 57=46+11

2160 59=15+44 57=57=57

2161 59=16+43 58+13=71

2162 59=17+42 58+14=72

2163 59=22+37 58+15=73

2164 59=23+36 58+16=74

2165 59=24+35 58+17=75

2166 59=25+34 58+18=76

2167 59=26+33 58+23=81

2168 59=27+32 58+24=82

2169 59=32+27 58+25=83

2170 59=33+26 58+26=84

2171 59=34+25 58+27=85

2172 59=35+24 58+28=86

2173 59=36+23 58=11+47

2174 59=37+22 58=12+46

2175 59=42+17 58=13+45

2176 59=43+16 58=14+44

2177 59=44+15 58=15+43

2178 59=45+14 58=16+42

2179 59=46+13 58=17+41

2180 59=47+12 58=21+37

2181 59=59=59 58=22+36

2182 6+1+4=11 58=23+35

2183 6+1+5=12 58=24+34

2184 6+1+6=13 58=25+33

2185 6+1+7=14 58=26+32

2186 6+1+9=16 58=27+31

2187 6+12=9+9 58=31+27

2188 6+2+3=11 58=32+26

2189 6+2+4=12 58=33+25

2190 6+2+5=13 58=34+24

2191 6+2+6=14 58=35+23

2192 6+2+7=15 58=36+22

2193 6+2+9=17 58=37+21

2194 6+3+2=11 58=41+17

2195 6+3+3=12 58=42+16

2196 6+3+4=13 58=43+15

2197 6+3+5=14 58=44+14

2198 6+3+6=15 58=45+13

2199 6+3+7=16 58=46+12

2200 6+4+1=11 58=47+11

2201 6+4+2=12 58=58=58

2202 6+4+3=13 6+1+4=11

2203 6+4+4=14 6+1+5=12

2204 6+4+5=15 6+1+6=13

2205 6+4+6=16 6+1+7=14

2206 6+4+7=17 6+1+8=15

2207 6+4+9=19 6+2+3=11

2208 6+5+1=12 6+2+4=12

2209 6+5+2=13 6+2+5=13

2210 6+5+3=14 6+2+6=14

2211 6+5+4=15 6+2+7=15

2212 6+5+5=16 6+2+8=16

2213 6+5+6=17 6+3+2=11

2214 6+6+1=13 6+3+3=12

2215 6+6+2=14 6+3+4=13

2216 6+6+3=15 6+3+5=14

2217 6+6+4=16 6+3+6=15

2218 6+6+5=17 6+3+7=16

2219 6+6+7=19 6+3+8=17

2220 6+6+9=21 6+4+1=11

2221 6+6=1+11 6+4+2=12

2222 6+6=11+1 6+4+3=13

2223 6+7+1=14 6+4+4=14

2224 6+7+2=15 6+4+5=15

2225 6+7+3=16 6+4+6=16

2226 6+7+4=17 6+4+7=17

2227 6+7+6=19 6+4+8=18

2228 6+7+9=22 6+5+1=12

2229 6+7=1+12 6+5+2=13

2230 6+7=11+2 6+5+3=14

2231 6+7=12+1 6+5+4=15

2232 6+7=2+11 6+5+5=16

2233 6+9+1=16 6+5+6=17

2234 6+9+2=17 6+5+7=18

2235 6+9+4=19 6+6+1=13

2236 6+9+6=21 6+6+2=14

2237 6+9+7=22 6+6+3=15

2238 6+9+9=24 6+6+4=16

2239 6+9=1+14 6+6+5=17

2240 6+9=11+4 6+6+6=18

2241 6+9=12+3 6+6=1+11

2242 6+9=13+2 6+6=11+1

2243 6+9=14+1 6+7+1=14

2244 6+9=2+13 6+7+2=15

2245 6+9=3+12 6+7+3=16

2246 6+9=4+11 6+7+4=17

2247 61+11=72 6+7+5=18

2248 61+12=73 6+7+8=21

2249 61+13=74 6+7=1+12

2250 61+14=75 6+7=11+2

2251 61+15=76 6+7=12+1

2252 61+16=77 6+7=2+11

2253 61+31=92 6+8+1=15

2254 61+32=93 6+8+2=16

2255 61+33=94 6+8+3=17

2256 61+34=95 6+8+4=18

2257 61+35=96 6+8+7=21

2258 61+36=97 6+8+8=22

2259 61=12+49 6+8=1+13

2260 61=14+47 6+8=11+3

2261 61=15+46 6+8=12+2

2262 61=16+45 6+8=13+1

2263 61=17+44 6+8=2+12

2264 61=19+42 6+8=3+11

2265 61=22+39 61+11=72

2266 61=24+37 61+12=73

2267 61=25+36 61+13=74

2268 61=26+35 61+14=75

2269 61=27+34 61+15=76

2270 61=29+32 61+16=77

2271 61=32+29 61+17=78

2272 61=34+27 61+21=82

2273 61=35+26 61+22=83

2274 61=36+25 61+23=84

2275 61=37+24 61+24=85

2276 61=39+22 61+25=86

2277 61=42+19 61+26=87

2278 61=44+17 61+27=88

2279 61=45+16 61=13+48

2280 61=46+15 61=14+47

2281 61=47+14 61=15+46

2282 61=49+12 61=16+45

2283 61=61=61 61=17+44

2284 62+11=73 61=18+43

2285 62+12=74 61=23+38

2286 62+13=75 61=24+37

2287 62+14=76 61=25+36

2288 62+15=77 61=26+35

2289 62+17=79 61=27+34

2290 62+29=91 61=28+33

2291 62+31=93 61=33+28

2292 62+32=94 61=34+27

2293 62+33=95 61=35+26

2294 62+34=96 61=36+25

2295 62+35=97 61=37+24

2296 62+37=99 61=38+23

2297 62=11+51 61=43+18

2298 62=13+49 61=44+17

2299 62=15+47 61=45+16

2300 62=16+46 61=46+15

2301 62=17+45 61=47+14

2302 62=19+43 61=48+13

2303 62=21+41 61=61=61

2304 62=23+39 62+11=73

2305 62=25+37 62+12=74

2306 62=26+36 62+13=75

2307 62=27+35 62+14=76

2308 62=29+33 62+15=77

2309 62=31+31 62+16=78

2310 62=33+29 62+21=83

2311 62=35+27 62+22=84

2312 62=36+26 62+23=85

2313 62=37+25 62+24=86

2314 62=39+23 62+25=87

2315 62=41+21 62+26=88

2316 62=43+19 62=11+51

2317 62=45+17 62=14+48

2318 62=46+16 62=15+47

2319 62=47+15 62=16+46

2320 62=49+13 62=17+45

2321 62=51+11 62=18+44

2322 62=62=62 62=21+41

2323 63+11=74 62=24+38

2324 63+12=75 62=25+37

2325 63+13=76 62=26+36

2326 63+14=77 62=27+35

2327 63+16=79 62=28+34

2328 63+29=92 62=31+31

2329 63+31=94 62=34+28

2330 63+32=95 62=35+27

2331 63+33=96 62=36+26

2332 63+34=97 62=37+25

2333 63+36=99 62=38+24

2334 63=11+52 62=41+21

2335 63=12+51 62=44+18

2336 63=14+49 62=45+17

2337 63=16+47 62=46+16

2338 63=17+46 62=47+15

2339 63=19+44 62=48+14

2340 63=21+42 62=51+11

2341 63=22+41 62=62=62

2342 63=24+39 63+11=74

2343 63=26+37 63+12=75

2344 63=27+36 63+13=76

2345 63=29+34 63+14=77

2346 63=31+32 63+15=78

2347 63=32+31 63+18=81

2348 63=34+29 63+21=84

2349 63=36+27 63+22=85

2350 63=37+26 63+23=86

2351 63=39+24 63+24=87

2352 63=41+22 63+25=88

2353 63=42+21 63=11+52

2354 63=44+19 63=12+51

2355 63=46+17 63=15+48

2356 63=47+16 63=16+47

2357 63=49+14 63=17+46

2358 63=51+12 63=18+45

2359 63=52+11 63=21+42

2360 63=63=63 63=22+41

2361 64+11=75 63=25+38

2362 64+12=76 63=26+37

2363 64+13=77 63=27+36

2364 64+15=79 63=28+35

2365 64+27=91 63=31+32

2366 64+29=93 63=32+31

2367 64+31=95 63=35+28

2368 64+32=96 63=36+27

2369 64+33=97 63=37+26

2370 64+35=99 63=38+25

2371 64=11+53 63=41+22

2372 64=12+52 63=42+21

2373 64=13+51 63=45+18

2374 64=15+49 63=46+17

2375 64=17+47 63=47+16

2376 64=19+45 63=48+15

2377 64=21+43 63=51+12

2378 64=22+42 63=52+11

2379 64=23+41 63=63=63

2380 64=25+39 64+11=75

2381 64=27+37 64+12=76

2382 64=29+35 64+13=77

2383 64=31+33 64+14=78

2384 64=32+32 64+17=81

2385 64=33+31 64+18=82

2386 64=35+29 64+21=85

2387 64=37+27 64+22=86

2388 64=39+25 64+23=87

2389 64=41+23 64+24=88

2390 64=42+22 64=11+53

2391 64=43+21 64=12+52

2392 64=45+19 64=13+51

2393 64=47+17 64=16+48

2394 64=49+15 64=17+47

2395 64=51+13 64=18+46

2396 64=52+12 64=21+43

2397 64=53+11 64=22+42

2398 64=64=64 64=23+41

2399 65+11=76 64=26+38

2400 65+12=77 64=27+37

2401 65+14=79 64=28+36

2402 65+26=91 64=31+33

2403 65+27=92 64=32+32

2404 65+29=94 64=33+31

2405 65+31=96 64=36+28

2406 65+32=97 64=37+27

2407 65+34=99 64=38+26

2408 65=11+54 64=41+23

2409 65=12+53 64=42+22

2410 65=13+52 64=43+21

2411 65=14+51 64=46+18

2412 65=16+49 64=47+17

2413 65=19+46 64=48+16

2414 65=21+44 64=51+13

2415 65=22+43 64=52+12

2416 65=23+42 64=53+11

2417 65=24+41 64=64=64

2418 65=26+39 65+11=76

2419 65=29+36 65+12=77

2420 65=31+34 65+13=78

2421 65=32+33 65+16=81

2422 65=33+32 65+17=82

2423 65=34+31 65+18=83

2424 65=36+29 65+21=86

2425 65=39+26 65+22=87

2426 65=41+24 65+23=88

2427 65=42+23 65=11+54

2428 65=43+22 65=12+53

2429 65=44+21 65=13+52

2430 65=46+19 65=14+51

2431 65=49+16 65=17+48

2432 65=51+14 65=18+47

2433 65=52+13 65=21+44

2434 65=53+12 65=22+43

2435 65=54+11 65=23+42

2436 65=65=65 65=24+41

2437 66+11=77 65=27+38

2438 66+13=79 65=28+37

2439 66+25=91 65=31+34

2440 66+26=92 65=32+33

2441 66+27=93 65=33+32

2442 66+29=95 65=34+31

2443 66+31=97 65=37+28

2444 66+33=99 65=38+27

2445 66=11+55 65=41+24

2446 66=12+54 65=42+23

2447 66=13+53 65=43+22

2448 66=14+52 65=44+21

2449 66=15+51 65=47+18

2450 66=17+49 65=48+17

2451 66=19+47 65=51+14

2452 66=21+45 65=52+13

2453 66=22+44 65=53+12

2454 66=23+43 65=54+11

2455 66=24+42 65=65=65

2456 66=25+41 66+11=77

2457 66=27+39 66+12=78

2458 66=29+37 66+15=81

2459 66=31+35 66+16=82

2460 66=32+34 66+17=83

2461 66=33+33 66+18=84

2462 66=34+32 66+21=87

2463 66=35+31 66+22=88

2464 66=37+29 66=11+55

2465 66=39+27 66=12+54

2466 66=41+25 66=13+53

2467 66=42+24 66=14+52

2468 66=43+23 66=15+51

2469 66=44+22 66=18+48

2470 66=45+21 66=21+45

2471 66=47+19 66=22+44

2472 66=49+17 66=23+43

2473 66=51+15 66=24+42

2474 66=52+14 66=25+41

2475 66=53+13 66=28+38

2476 66=54+12 66=31+35

2477 66=55+11 66=32+34

2478 66=66=66 66=33+33

2479 67+12=79 66=34+32

2480 67+24=91 66=35+31

2481 67+25=92 66=38+28

2482 67+26=93 66=41+25

2483 67+27=94 66=42+24

2484 67+29=96 66=43+23

2485 67+32=99 66=44+22

2486 67=11+56 66=45+21

2487 67=12+55 66=48+18

2488 67=13+54 66=51+15

2489 67=14+53 66=52+14

2490 67=15+52 66=53+13

2491 67=16+51 66=54+12

2492 67=21+46 66=55+11

2493 67=22+45 66=66=66

2494 67=23+44 67+11=78

2495 67=24+43 67+14=81

2496 67=25+42 67+15=82

2497 67=26+41 67+16=83

2498 67=31+36 67+17=84

2499 67=32+35 67+18=85

2500 67=33+34 67+21=88

2501 67=34+33 67=11+56

2502 67=35+32 67=12+55

2503 67=36+31 67=13+54

2504 67=41+26 67=14+53

2505 67=42+25 67=15+52

2506 67=43+24 67=16+51

2507 67=44+23 67=21+46

2508 67=45+22 67=22+45

2509 67=46+21 67=23+44

2510 67=51+16 67=24+43

2511 67=52+15 67=25+42

2512 67=53+14 67=26+41

2513 67=54+13 67=31+36

2514 67=55+12 67=32+35

2515 67=56+11 67=33+34

2516 67=67=67 67=34+33

2517 69+22=91 67=35+32

2518 69+23=92 67=36+31

2519 69+24=93 67=41+26

2520 69+25=94 67=42+25

2521 69+26=95 67=43+24

2522 69+27=96 67=44+23

2523 69=12+57 67=45+22

2524 69=13+56 67=46+21

2525 69=14+55 67=51+16

2526 69=15+54 67=52+15

2527 69=16+53 67=53+14

2528 69=17+52 67=54+13

2529 69=22+47 67=55+12

2530 69=23+46 67=56+11

2531 69=24+45 67=67=67

2532 69=25+44 68+13=81

2533 69=26+43 68+14=82

2534 69=27+42 68+15=83

2535 69=32+37 68+16=84

2536 69=33+36 68+17=85

2537 69=34+35 68+18=86

2538 69=35+34 68=11+57

2539 69=36+33 68=12+56

2540 69=37+32 68=13+55

2541 69=42+27 68=14+54

2542 69=43+26 68=15+53

2543 69=44+25 68=16+52

2544 69=45+24 68=17+51

2545 69=46+23 68=21+47

2546 69=47+22 68=22+46

2547 69=52+17 68=23+45

2548 69=53+16 68=24+44

2549 69=54+15 68=25+43

2550 69=55+14 68=26+42

2551 69=56+13 68=27+41

2552 69=57+12 68=31+37

2553 69=69=69 68=32+36

2554 7+1+3=11 68=33+35

2555 7+1+4=12 68=34+34

2556 7+1+5=13 68=35+33

2557 7+1+6=14 68=36+32

2558 7+1+7=15 68=37+31

2559 7+1+9=17 68=41+27

2560 7+11=9+9 68=42+26

2561 7+2+2=11 68=43+25

2562 7+2+3=12 68=44+24

2563 7+2+4=13 68=45+23

2564 7+2+5=14 68=46+22

2565 7+2+6=15 68=47+21

2566 7+2+7=16 68=51+17

2567 7+3+1=11 68=52+16

2568 7+3+2=12 68=53+15

2569 7+3+3=13 68=54+14

2570 7+3+4=14 68=55+13

2571 7+3+5=15 68=56+12

2572 7+3+6=16 68=57+11

2573 7+3+7=17 68=68=68

2574 7+3+9=19 7+1+3=11

2575 7+4+1=12 7+1+4=12

2576 7+4+2=13 7+1+5=13

2577 7+4+3=14 7+1+6=14

2578 7+4+4=15 7+1+7=15

2579 7+4+5=16 7+1+8=16

2580 7+4+6=17 7+2+2=11

2581 7+5+1=13 7+2+3=12

2582 7+5+2=14 7+2+4=13

2583 7+5+3=15 7+2+5=14

2584 7+5+4=16 7+2+6=15

2585 7+5+5=17 7+2+7=16

2586 7+5+7=19 7+2+8=17

2587 7+5+9=21 7+3+1=11

2588 7+5=1+11 7+3+2=12

2589 7+5=11+1 7+3+3=13

2590 7+6+1=14 7+3+4=14

2591 7+6+2=15 7+3+5=15

2592 7+6+3=16 7+3+6=16

2593 7+6+4=17 7+3+7=17

2594 7+6+6=19 7+3+8=18

2595 7+6+9=22 7+4+1=12

2596 7+6=1+12 7+4+2=13

2597 7+6=11+2 7+4+3=14

2598 7+6=12+1 7+4+4=15

2599 7+6=2+11 7+4+5=16

2600 7+7+1=15 7+4+6=17

2601 7+7+2=16 7+4+7=18

2602 7+7+3=17 7+5+1=13

2603 7+7+5=19 7+5+2=14

2604 7+7+7=21 7+5+3=15

2605 7+7+9=23 7+5+4=16

2606 7+7=1+13 7+5+5=17

2607 7+7=11+3 7+5+6=18

2608 7+7=12+2 7+5=1+11

2609 7+7=13+1 7+5=11+1

2610 7+7=2+12 7+6+1=14

2611 7+7=3+11 7+6+2=15

2612 7+9+1=17 7+6+3=16

2613 7+9+3=19 7+6+4=17

2614 7+9+5=21 7+6+5=18

2615 7+9+6=22 7+6+8=21

2616 7+9+7=23 7+6=1+12

2617 7+9+9=25 7+6=11+2

2618 7+9=1+15 7+6=12+1

2619 7+9=11+5 7+6=2+11

2620 7+9=12+4 7+7+1=15

2621 7+9=13+3 7+7+2=16

2622 7+9=14+2 7+7+3=17

2623 7+9=15+1 7+7+4=18

2624 7+9=2+14 7+7+7=21

2625 7+9=3+13 7+7+8=22

2626 7+9=4+12 7+7=1+13

2627 7+9=5+11 7+7=11+3

2628 71+21=92 7+7=12+2

2629 71+22=93 7+7=13+1

2630 71+23=94 7+7=2+12

2631 71+24=95 7+7=3+11

2632 71+25=96 7+8+1=16

2633 71+26=97 7+8+2=17

2634 71=12+59 7+8+3=18

2635 71=14+57 7+8+6=21

2636 71=15+56 7+8+7=22

2637 71=16+55 7+8+8=23

2638 71=17+54 7+8=1+14

2639 71=19+52 7+8=11+4

2640 71=22+49 7+8=12+3

2641 71=24+47 7+8=13+2

2642 71=25+46 7+8=14+1

2643 71=26+45 7+8=2+13

2644 71=27+44 7+8=3+12

2645 71=29+42 7+8=4+11

2646 71=32+39 71+11=82

2647 71=34+37 71+12=83

2648 71=35+36 71+13=84

2649 71=36+35 71+14=85

2650 71=37+34 71+15=86

2651 71=39+32 71+16=87

2652 71=42+29 71+17=88

2653 71=44+27 71=13+58

2654 71=45+26 71=14+57

2655 71=46+25 71=15+56

2656 71=47+24 71=16+55

2657 71=49+22 71=17+54

2658 71=52+19 71=18+53

2659 71=54+17 71=23+48

2660 71=55+16 71=24+47

2661 71=56+15 71=25+46

2662 71=57+14 71=26+45

2663 71=59+12 71=27+44

2664 71=71=71 71=28+43

2665 72+19=91 71=33+38

2666 72+21=93 71=34+37

2667 72+22=94 71=35+36

2668 72+23=95 71=36+35

2669 72+24=96 71=37+34

2670 72+25=97 71=38+33

2671 72+27=99 71=43+28

2672 72=11+61 71=44+27

2673 72=13+59 71=45+26

2674 72=15+57 71=46+25

2675 72=16+56 71=47+24

2676 72=17+55 71=48+23

2677 72=19+53 71=53+18

2678 72=21+51 71=54+17

2679 72=23+49 71=55+16

2680 72=25+47 71=56+15

2681 72=26+46 71=57+14

2682 72=27+45 71=58+13

2683 72=29+43 71=71=71

2684 72=31+41 72+11=83

2685 72=33+39 72+12=84

2686 72=35+37 72+13=85

2687 72=36+36 72+14=86

2688 72=37+35 72+15=87

2689 72=39+33 72+16=88

2690 72=41+31 72=11+61

2691 72=43+29 72=14+58

2692 72=45+27 72=15+57

2693 72=46+26 72=16+56

2694 72=47+25 72=17+55

2695 72=49+23 72=18+54

2696 72=51+21 72=21+51

2697 72=53+19 72=24+48

2698 72=55+17 72=25+47

2699 72=56+16 72=26+46

2700 72=57+15 72=27+45

2701 72=59+13 72=28+44

2702 72=61+11 72=31+41

2703 72=72=72 72=34+38

2704 73+19=92 72=35+37

2705 73+21=94 72=36+36

2706 73+22=95 72=37+35

2707 73+23=96 72=38+34

2708 73+24=97 72=41+31

2709 73+26=99 72=44+28

2710 73=11+62 72=45+27

2711 73=12+61 72=46+26

2712 73=14+59 72=47+25

2713 73=16+57 72=48+24

2714 73=17+56 72=51+21

2715 73=19+54 72=54+18

2716 73=21+52 72=55+17

2717 73=22+51 72=56+16

2718 73=24+49 72=57+15

2719 73=26+47 72=58+14

2720 73=27+46 72=61+11

2721 73=29+44 72=72=72

2722 73=31+42 73+11=84

2723 73=32+41 73+12=85

2724 73=34+39 73+13=86

2725 73=36+37 73+14=87

2726 73=37+36 73+15=88

2727 73=39+34 73=11+62

2728 73=41+32 73=12+61

2729 73=42+31 73=15+58

2730 73=44+29 73=16+57

2731 73=46+27 73=17+56

2732 73=47+26 73=18+55

2733 73=49+24 73=21+52

2734 73=51+22 73=22+51

2735 73=52+21 73=25+48

2736 73=54+19 73=26+47

2737 73=56+17 73=27+46

2738 73=57+16 73=28+45

2739 73=59+14 73=31+42

2740 73=61+12 73=32+41

2741 73=62+11 73=35+38

2742 73=73=73 73=36+37

2743 74+17=91 73=37+36

2744 74+19=93 73=38+35

2745 74+21=95 73=41+32

2746 74+22=96 73=42+31

2747 74+23=97 73=45+28

2748 74+25=99 73=46+27

2749 74=11+63 73=47+26

2750 74=12+62 73=48+25

2751 74=13+61 73=51+22

2752 74=15+59 73=52+21

2753 74=17+57 73=55+18

2754 74=19+55 73=56+17

2755 74=21+53 73=57+16

2756 74=22+52 73=58+15

2757 74=23+51 73=61+12

2758 74=25+49 73=62+11

2759 74=27+47 73=73=73

2760 74=29+45 74+11=85

2761 74=31+43 74+12=86

2762 74=32+42 74+13=87

2763 74=33+41 74+14=88

2764 74=35+39 74=11+63

2765 74=37+37 74=12+62

2766 74=39+35 74=13+61

2767 74=41+33 74=16+58

2768 74=42+32 74=17+57

2769 74=43+31 74=18+56

2770 74=45+29 74=21+53

2771 74=47+27 74=22+52

2772 74=49+25 74=23+51

2773 74=51+23 74=26+48

2774 74=52+22 74=27+47

2775 74=53+21 74=28+46

2776 74=55+19 74=31+43

2777 74=57+17 74=32+42

2778 74=59+15 74=33+41

2779 74=61+13 74=36+38

2780 74=62+12 74=37+37

2781 74=63+11 74=38+36

2782 74=74=74 74=41+33

2783 75+16=91 74=42+32

2784 75+17=92 74=43+31

2785 75+19=94 74=46+28

2786 75+21=96 74=47+27

2787 75+22=97 74=48+26

2788 75+24=99 74=51+23

2789 75=11+64 74=52+22

2790 75=12+63 74=53+21

2791 75=13+62 74=56+18

2792 75=14+61 74=57+17

2793 75=16+59 74=58+16

2794 75=19+56 74=61+13

2795 75=21+54 74=62+12

2796 75=22+53 74=63+11

2797 75=23+52 74=74=74

2798 75=24+51 75+11=86

2799 75=26+49 75+12=87

2800 75=29+46 75+13=88

2801 75=31+44 75=11+64

2802 75=32+43 75=12+63

2803 75=33+42 75=13+62

2804 75=34+41 75=14+61

2805 75=36+39 75=17+58

2806 75=39+36 75=18+57

2807 75=41+34 75=21+54

2808 75=42+33 75=22+53

2809 75=43+32 75=23+52

2810 75=44+31 75=24+51

2811 75=46+29 75=27+48

2812 75=49+26 75=28+47

2813 75=51+24 75=31+44

2814 75=52+23 75=32+43

2815 75=53+22 75=33+42

2816 75=54+21 75=34+41

2817 75=56+19 75=37+38

2818 75=59+16 75=38+37

2819 75=61+14 75=41+34

2820 75=62+13 75=42+33

2821 75=63+12 75=43+32

2822 75=64+11 75=44+31

2823 75=75=75 75=47+28

2824 76+15=91 75=48+27

2825 76+16=92 75=51+24

2826 76+17=93 75=52+23

2827 76+19=95 75=53+22

2828 76+21=97 75=54+21

2829 76+23=99 75=57+18

2830 76=11+65 75=58+17

2831 76=12+64 75=61+14

2832 76=13+63 75=62+13

2833 76=14+62 75=63+12

2834 76=15+61 75=64+11

2835 76=17+59 75=75=75

2836 76=19+57 76+11=87

2837 76=21+55 76+12=88

2838 76=22+54 76=11+65

2839 76=23+53 76=12+64

2840 76=24+52 76=13+63

2841 76=25+51 76=14+62

2842 76=27+49 76=15+61

2843 76=29+47 76=18+58

2844 76=31+45 76=21+55

2845 76=32+44 76=22+54

2846 76=33+43 76=23+53

2847 76=34+42 76=24+52

2848 76=35+41 76=25+51

2849 76=37+39 76=28+48

2850 76=39+37 76=31+45

2851 76=41+35 76=32+44

2852 76=42+34 76=33+43

2853 76=43+33 76=34+42

2854 76=44+32 76=35+41

2855 76=45+31 76=38+38

2856 76=47+29 76=41+35

2857 76=49+27 76=42+34

2858 76=51+25 76=43+33

2859 76=52+24 76=44+32

2860 76=53+23 76=45+31

2861 76=54+22 76=48+28

2862 76=55+21 76=51+25

2863 76=57+19 76=52+24

2864 76=59+17 76=53+23

2865 76=61+15 76=54+22

2866 76=62+14 76=55+21

2867 76=63+13 76=58+18

2868 76=64+12 76=61+15

2869 76=65+11 76=62+14

2870 76=76=76 76=63+13

2871 77+14=91 76=64+12

2872 77+15=92 76=65+11

2873 77+16=93 76=76=76

2874 77+17=94 77+11=88

2875 77+19=96 77=11+66

2876 77+22=99 77=12+65

2877 77=11+66 77=13+64

2878 77=12+65 77=14+63

2879 77=13+64 77=15+62

2880 77=14+63 77=16+61

2881 77=15+62 77=21+56

2882 77=16+61 77=22+55

2883 77=21+56 77=23+54

2884 77=22+55 77=24+53

2885 77=23+54 77=25+52

2886 77=24+53 77=26+51

2887 77=25+52 77=31+46

2888 77=26+51 77=32+45

2889 77=31+46 77=33+44

2890 77=32+45 77=34+43

2891 77=33+44 77=35+42

2892 77=34+43 77=36+41

2893 77=35+42 77=41+36

2894 77=36+41 77=42+35

2895 77=41+36 77=43+34

2896 77=42+35 77=44+33

2897 77=43+34 77=45+32

2898 77=44+33 77=46+31

2899 77=45+32 77=51+26

2900 77=46+31 77=52+25

2901 77=51+26 77=53+24

2902 77=52+25 77=54+23

2903 77=53+24 77=55+22

2904 77=54+23 77=56+21

2905 77=55+22 77=61+16

2906 77=56+21 77=62+15

2907 77=61+16 77=63+14

2908 77=62+15 77=64+13

2909 77=63+14 77=65+12

2910 77=64+13 77=66+11

2911 77=65+12 77=77=77

2912 77=66+11 78=11+67

2913 77=77=77 78=12+66

2914 79+12=91 78=13+65

2915 79+13=92 78=14+64

2916 79+14=93 78=15+63

2917 79+15=94 78=16+62

2918 79+16=95 78=17+61

2919 79+17=96 78=21+57

2920 79=12+67 78=22+56

2921 79=13+66 78=23+55

2922 79=14+65 78=24+54

2923 79=15+64 78=25+53

2924 79=16+63 78=26+52

2925 79=17+62 78=27+51

2926 79=22+57 78=31+47

2927 79=23+56 78=32+46

2928 79=24+55 78=33+45

2929 79=25+54 78=34+44

2930 79=26+53 78=35+43

2931 79=27+52 78=36+42

2932 79=32+47 78=37+41

2933 79=33+46 78=41+37

2934 79=34+45 78=42+36

2935 79=35+44 78=43+35

2936 79=36+43 78=44+34

2937 79=37+42 78=45+33

2938 79=42+37 78=46+32

2939 79=43+36 78=47+31

2940 79=44+35 78=51+27

2941 79=45+34 78=52+26

2942 79=46+33 78=53+25

2943 79=47+32 78=54+24

2944 79=52+27 78=55+23

2945 79=53+26 78=56+22

2946 79=54+25 78=57+21

2947 79=55+24 78=61+17

2948 79=56+23 78=62+16

2949 79=57+22 78=63+15

2950 79=62+17 78=64+14

2951 79=63+16 78=65+13

2952 79=64+15 78=66+12

2953 79=65+14 78=67+11

2954 79=66+13 78=78=78

2955 79=67+12 8+1+2=11

2956 79=79=79 8+1+3=12

2957 9+1+1=11 8+1+4=13

2958 9+1+2=12 8+1+5=14

2959 9+1+3=13 8+1+6=15

2960 9+1+4=14 8+1+7=16

2961 9+1+5=15 8+1+8=17

2962 9+1+6=16 8+2+1=11

2963 9+1+7=17 8+2+2=12

2964 9+1+9=19 8+2+3=13

2965 9+2+1=12 8+2+4=14

2966 9+2+2=13 8+2+5=15

2967 9+2+3=14 8+2+6=16

2968 9+2+4=15 8+2+7=17

2969 9+2+5=16 8+2+8=18

2970 9+2+6=17 8+3+1=12

2971 9+3+1=13 8+3+2=13

2972 9+3+2=14 8+3+3=14

2973 9+3+3=15 8+3+4=15

2974 9+3+4=16 8+3+5=16

2975 9+3+5=17 8+3+6=17

2976 9+3+7=19 8+3+7=18

2977 9+3+9=21 8+4+1=13

2978 9+3=1+11 8+4+2=14

2979 9+3=11+1 8+4+3=15

2980 9+4+1=14 8+4+4=16

2981 9+4+2=15 8+4+5=17

2982 9+4+3=16 8+4+6=18

2983 9+4+4=17 8+4=1+11

2984 9+4+6=19 8+4=11+1

2985 9+4+9=22 8+5+1=14

2986 9+4=1+12 8+5+2=15

2987 9+4=11+2 8+5+3=16

2988 9+4=12+1 8+5+4=17

2989 9+4=2+11 8+5+5=18

2990 9+5+1=15 8+5+8=21

2991 9+5+2=16 8+5=1+12

2992 9+5+3=17 8+5=11+2

2993 9+5+5=19 8+5=12+1

2994 9+5+7=21 8+5=2+11

2995 9+5+9=23 8+6+1=15

2996 9+5=1+13 8+6+2=16

2997 9+5=11+3 8+6+3=17

2998 9+5=12+2 8+6+4=18

2999 9+5=13+1 8+6+7=21

3000 9+5=2+12 8+6+8=22

3001 9+5=3+11 8+6=1+13

3002 9+6+1=16 8+6=11+3

3003 9+6+2=17 8+6=12+2

3004 9+6+4=19 8+6=13+1

3005 9+6+6=21 8+6=2+12

3006 9+6+7=22 8+6=3+11

3007 9+6+9=24 8+7+1=16

3008 9+6=1+14 8+7+2=17

3009 9+6=11+4 8+7+3=18

3010 9+6=12+3 8+7+6=21

3011 9+6=13+2 8+7+7=22

3012 9+6=14+1 8+7+8=23

3013 9+6=2+13 8+7=1+14

3014 9+6=3+12 8+7=11+4

3015 9+6=4+11 8+7=12+3

3016 9+7+1=17 8+7=13+2

3017 9+7+3=19 8+7=14+1

3018 9+7+5=21 8+7=2+13

3019 9+7+6=22 8+7=3+12

3020 9+7+7=23 8+7=4+11

3021 9+7+9=25 8+8+1=17

3022 9+7=1+15 8+8+2=18

3023 9+7=11+5 8+8+5=21

3024 9+7=12+4 8+8+6=22

3025 9+7=13+3 8+8+7=23

3026 9+7=14+2 8+8+8=24

3027 9+7=15+1 8+8=1+15

3028 9+7=2+14 8+8=11+5

3029 9+7=3+13 8+8=12+4

3030 9+7=4+12 8+8=13+3

3031 9+7=5+11 8+8=14+2

3032 9+9+1=19 8+8=15+1

3033 9+9+3=21 8+8=2+14

3034 9+9+4=22 8+8=3+13

3035 9+9+5=23 8+8=4+12

3036 9+9+6=24 8+8=5+11

3037 9+9+7=25 81=13+68

3038 9+9+9=27 81=14+67

3039 9+9=1+17 81=15+66

3040 9+9=11+7 81=16+65

3041 9+9=12+6 81=17+64

3042 9+9=13+5 81=18+63

3043 9+9=14+4 81=23+58

3044 9+9=15+3 81=24+57

3045 9+9=16+2 81=25+56

3046 9+9=17+1 81=26+55

3047 9+9=2+16 81=27+54

3048 9+9=3+15 81=28+53

3049 9+9=4+14 81=33+48

3050 9+9=5+13 81=34+47

3051 9+9=6+12 81=35+46

3052 9+9=7+11 81=36+45

3053 91=12+79 81=37+44

3054 91=14+77 81=38+43

3055 91=15+76 81=43+38

3056 91=16+75 81=44+37

3057 91=17+74 81=45+36

3058 91=19+72 81=46+35

3059 91=22+69 81=47+34

3060 91=24+67 81=48+33

3061 91=25+66 81=53+28

3062 91=26+65 81=54+27

3063 91=27+64 81=55+26

3064 91=29+62 81=56+25

3065 91=32+59 81=57+24

3066 91=34+57 81=58+23

3067 91=35+56 81=63+18

3068 91=36+55 81=64+17

3069 91=37+54 81=65+16

3070 91=39+52 81=66+15

3071 91=42+49 81=67+14

3072 91=44+47 81=68+13

3073 91=45+46 81=81=81

3074 91=46+45 82=11+71

3075 91=47+44 82=14+68

3076 91=49+42 82=15+67

3077 91=52+39 82=16+66

3078 91=54+37 82=17+65

3079 91=55+36 82=18+64

3080 91=56+35 82=21+61

3081 91=57+34 82=24+58

3082 91=59+32 82=25+57

3083 91=62+29 82=26+56

3084 91=64+27 82=27+55

3085 91=65+26 82=28+54

3086 91=66+25 82=31+51

3087 91=67+24 82=34+48

3088 91=69+22 82=35+47

3089 91=72+19 82=36+46

3090 91=74+17 82=37+45

3091 91=75+16 82=38+44

3092 91=76+15 82=41+41

3093 91=77+14 82=44+38

3094 91=79+12 82=45+37

3095 91=91=91 82=46+36

3096 92=13+79 82=47+35

3097 92=15+77 82=48+34

3098 92=16+76 82=51+31

3099 92=17+75 82=54+28

3100 92=19+73 82=55+27

3101 92=21+71 82=56+26

3102 92=23+69 82=57+25

3103 92=25+67 82=58+24

3104 92=26+66 82=61+21

3105 92=27+65 82=64+18

3106 92=29+63 82=65+17

3107 92=31+61 82=66+16

3108 92=33+59 82=67+15

3109 92=35+57 82=68+14

3110 92=36+56 82=71+11

3111 92=37+55 82=82=82

3112 92=39+53 83=11+72

3113 92=41+51 83=12+71

3114 92=43+49 83=15+68

3115 92=45+47 83=16+67

3116 92=46+46 83=17+66

3117 92=47+45 83=18+65

3118 92=49+43 83=21+62

3119 92=51+41 83=22+61

3120 92=53+39 83=25+58

3121 92=55+37 83=26+57

3122 92=56+36 83=27+56

3123 92=57+35 83=28+55

3124 92=59+33 83=31+52

3125 92=61+31 83=32+51

3126 92=63+29 83=35+48

3127 92=65+27 83=36+47

3128 92=66+26 83=37+46

3129 92=67+25 83=38+45

3130 92=69+23 83=41+42

3131 92=71+21 83=42+41

3132 92=73+19 83=45+38

3133 92=75+17 83=46+37

3134 92=76+16 83=47+36

3135 92=77+15 83=48+35

3136 92=79+13 83=51+32

3137 92=92=92 83=52+31

3138 93=14+79 83=55+28

3139 93=16+77 83=56+27

3140 93=17+76 83=57+26

3141 93=19+74 83=58+25

3142 93=21+72 83=61+22

3143 93=22+71 83=62+21

3144 93=24+69 83=65+18

3145 93=26+67 83=66+17

3146 93=27+66 83=67+16

3147 93=29+64 83=68+15

3148 93=31+62 83=71+12

3149 93=32+61 83=72+11

3150 93=34+59 83=83=83

3151 93=36+57 84=11+73

3152 93=37+56 84=12+72

3153 93=39+54 84=13+71

3154 93=41+52 84=16+68

3155 93=42+51 84=17+67

3156 93=44+49 84=18+66

3157 93=46+47 84=21+63

3158 93=47+46 84=22+62

3159 93=49+44 84=23+61

3160 93=51+42 84=26+58

3161 93=52+41 84=27+57

3162 93=54+39 84=28+56

3163 93=56+37 84=31+53

3164 93=57+36 84=32+52

3165 93=59+34 84=33+51

3166 93=61+32 84=36+48

3167 93=62+31 84=37+47

3168 93=64+29 84=38+46

3169 93=66+27 84=41+43

3170 93=67+26 84=42+42

3171 93=69+24 84=43+41

3172 93=71+22 84=46+38

3173 93=72+21 84=47+37

3174 93=74+19 84=48+36

3175 93=76+17 84=51+33

3176 93=77+16 84=52+32

3177 93=79+14 84=53+31

3178 93=93=93 84=56+28

3179 94=15+79 84=57+27

3180 94=17+77 84=58+26

3181 94=19+75 84=61+23

3182 94=21+73 84=62+22

3183 94=22+72 84=63+21

3184 94=23+71 84=66+18

3185 94=25+69 84=67+17

3186 94=27+67 84=68+16

3187 94=29+65 84=71+13

3188 94=31+63 84=72+12

3189 94=32+62 84=73+11

3190 94=33+61 84=84=84

3191 94=35+59 85=11+74

3192 94=37+57 85=12+73

3193 94=39+55 85=13+72

3194 94=41+53 85=14+71

3195 94=42+52 85=17+68

3196 94=43+51 85=18+67

3197 94=45+49 85=21+64

3198 94=47+47 85=22+63

3199 94=49+45 85=23+62

3200 94=51+43 85=24+61

3201 94=52+42 85=27+58

3202 94=53+41 85=28+57

3203 94=55+39 85=31+54

3204 94=57+37 85=32+53

3205 94=59+35 85=33+52

3206 94=61+33 85=34+51

3207 94=62+32 85=37+48

3208 94=63+31 85=38+47

3209 94=65+29 85=41+44

3210 94=67+27 85=42+43

3211 94=69+25 85=43+42

3212 94=71+23 85=44+41

3213 94=72+22 85=47+38

3214 94=73+21 85=48+37

3215 94=75+19 85=51+34

3216 94=77+17 85=52+33

3217 94=79+15 85=53+32

3218 94=94=94 85=54+31

3219 95=16+79 85=57+28

3220 95=19+76 85=58+27

3221 95=21+74 85=61+24

3222 95=22+73 85=62+23

3223 95=23+72 85=63+22

3224 95=24+71 85=64+21

3225 95=26+69 85=67+18

3226 95=29+66 85=68+17

3227 95=31+64 85=71+14

3228 95=32+63 85=72+13

3229 95=33+62 85=73+12

3230 95=34+61 85=74+11

3231 95=36+59 85=85=85

3232 95=39+56 86=11+75

3233 95=41+54 86=12+74

3234 95=42+53 86=13+73

3235 95=43+52 86=14+72

3236 95=44+51 86=15+71

3237 95=46+49 86=18+68

3238 95=49+46 86=21+65

3239 95=51+44 86=22+64

3240 95=52+43 86=23+63

3241 95=53+42 86=24+62

3242 95=54+41 86=25+61

3243 95=56+39 86=28+58

3244 95=59+36 86=31+55

3245 95=61+34 86=32+54

3246 95=62+33 86=33+53

3247 95=63+32 86=34+52

3248 95=64+31 86=35+51

3249 95=66+29 86=38+48

3250 95=69+26 86=41+45

3251 95=71+24 86=42+44

3252 95=72+23 86=43+43

3253 95=73+22 86=44+42

3254 95=74+21 86=45+41

3255 95=76+19 86=48+38

3256 95=79+16 86=51+35

3257 95=95=95 86=52+34

3258 96=17+79 86=53+33

3259 96=19+77 86=54+32

3260 96=21+75 86=55+31

3261 96=22+74 86=58+28

3262 96=23+73 86=61+25

3263 96=24+72 86=62+24

3264 96=25+71 86=63+23

3265 96=27+69 86=64+22

3266 96=29+67 86=65+21

3267 96=31+65 86=68+18

3268 96=32+64 86=71+15

3269 96=33+63 86=72+14

3270 96=34+62 86=73+13

3271 96=35+61 86=74+12

3272 96=37+59 86=75+11

3273 96=39+57 86=86=86

3274 96=41+55 87=11+76

3275 96=42+54 87=12+75

3276 96=43+53 87=13+74

3277 96=44+52 87=14+73

3278 96=45+51 87=15+72

3279 96=47+49 87=16+71

3280 96=49+47 87=21+66

3281 96=51+45 87=22+65

3282 96=52+44 87=23+64

3283 96=53+43 87=24+63

3284 96=54+42 87=25+62

3285 96=55+41 87=26+61

3286 96=57+39 87=31+56

3287 96=59+37 87=32+55

3288 96=61+35 87=33+54

3289 96=62+34 87=34+53

3290 96=63+33 87=35+52

3291 96=64+32 87=36+51

3292 96=65+31 87=41+46

3293 96=67+29 87=42+45

3294 96=69+27 87=43+44

3295 96=71+25 87=44+43

3296 96=72+24 87=45+42

3297 96=73+23 87=46+41

3298 96=74+22 87=51+36

3299 96=75+21 87=52+35

3300 96=77+19 87=53+34

3301 96=79+17 87=54+33

3302 96=96=96 87=55+32

3303 97=21+76 87=56+31

3304 97=22+75 87=61+26

3305 97=23+74 87=62+25

3306 97=24+73 87=63+24

3307 97=25+72 87=64+23

3308 97=26+71 87=65+22

3309 97=31+66 87=66+21

3310 97=32+65 87=71+16

3311 97=33+64 87=72+15

3312 97=34+63 87=73+14

3313 97=35+62 87=74+13

3314 97=36+61 87=75+12

3315 97=41+56 87=76+11

3316 97=42+55 87=87=87

3317 97=43+54 88=11+77

3318 97=44+53 88=12+76

3319 97=45+52 88=13+75

3320 97=46+51 88=14+74

3321 97=51+46 88=15+73

3322 97=52+45 88=16+72

3323 97=53+44 88=17+71

3324 97=54+43 88=21+67

3325 97=55+42 88=22+66

3326 97=56+41 88=23+65

3327 97=61+36 88=24+64

3328 97=62+35 88=25+63

3329 97=63+34 88=26+62

3330 97=64+33 88=27+61

3331 97=65+32 88=31+57

3332 97=66+31 88=32+56

3333 97=71+26 88=33+55

3334 97=72+25 88=34+54

3335 97=73+24 88=35+53

3336 97=74+23 88=36+52

3337 97=75+22 88=37+51

3338 97=76+21 88=41+47

3339 97=97=97 88=42+46

3340 99=22+77 88=43+45

3341 99=23+76 88=44+44

3342 99=24+75 88=45+43

3343 99=25+74 88=46+42

3344 99=26+73 88=47+41

3345 99=27+72 88=51+37

3346 99=32+67 88=52+36

3347 99=33+66 88=53+35

3348 99=34+65 88=54+34

3349 99=35+64 88=55+33

3350 99=36+63 88=56+32

3351 99=37+62 88=57+31

3352 99=42+57 88=61+27

3353 99=43+56 88=62+26

3354 99=44+55 88=63+25

3355 99=45+54 88=64+24

3356 99=46+53 88=65+23

3357 99=47+52 88=66+22

3358 99=52+47 88=67+21

3359 99=53+46 88=71+17

3360 99=54+45 88=72+16

3361 99=55+44 88=73+15

3362 99=56+43 88=74+14

3363 99=57+42 88=75+13

3364 99=62+37 88=76+12

3365 99=63+36 88=77+11

3366 99=64+35 88=88=88

3367 99=65+34

3368 99=66+33

3369 99=67+32

3370 99=72+27

3371 99=73+26

3372 99=74+25

3373 99=75+24

3374 99=76+23

3375 99=77+22

3376 99=99=99

 

 

[0+8=] gives thus the longest finite sequence of 8-digit integers:

 

S(8) = 10109811, 10118309, 10118507, 10118606, 10118705, 10118903, 10128409, 10128607, 10128706, 10128904, 10138509, 10138707, 10138905, 10148609, 10148906, 10158709, 10158907, 10178909, 10209812, 10307811, 10309813, 10406811, 10407812, 10409814, 10505811, 10506812, 10507813, 10509815, 10604811, 10605812, 10606813, 10607814, 10609816, 10703811, 10704812, 10705813, 10706814, 10707815, 10709817, 10901811, 10902812, 10903813, 10904814, 10905815, 10906816, 10907817, 10909819, 11011822, 11012823, 11013824, 11014825, 11015826, 11016827, 11018309, 11018507, 11018606, 11018705, 11018903, 11021832, 11022833, 11023834, 11024835, 11025836, 11026837, 11028409, 11028607, 11028706, 11028904, 11031842, 11032843, 11033844, 11034845, 11035846, 11036847, 11038509, 11038707, 11038905, 11041852, 11042853, 11043854, 11044855, 11045856, 11046857, 11048609, 11048906, 11051862, 11052863, 11053864, 11054865, 11055866, 11056867, 11058709, 11058907, 11061872, 11062873, 11063874, 11064875, 11065876, 11066877, 11078909, 11810109, 11810307, 11810406, 11810505, 11810604, 11810703, 11810901, 11811811, 11820207, 11820306, 11820405, 11820504, 11820603, 11820702, 11830107, 11830206, 11830305, 11830404, 11830503, 11830602, 11830701, 11840106, 11840205, 11840304, 11840403, 11840502, 11840601, 11850105, 11850204, 11850303, 11850402, 11850501, 11860104, 11860203, 11860302, 11860401, 11870103, 11870202, 11870301, 11890101, 12011823, 12012824, 12013825, 12014826, 12015827, 12017829, 12018409, 12018607, 12018706, 12018904, 12019831, 12021833, 12022834, 12023835, 12024836, 12025837, 12027839, 12028509, 12028707, 12028905, 12029841, 12031843, 12032844, 12033845, 12034846, 12035847, 12037849, 12038609, 12038906, 12039851, 12041853, 12042854, 12043855, 12044856, 12045857, 12047859, 12048709, 12048907, 12049861, 12051863, 12052864, 12053865, 12054866, 12055867, 12057869, 12059871, 12061873, 12062874, 12063875, 12064876, 12065877, 12067879, 12068909, 12079891, 12810209, 12810407, 12810506, 12810605, 12810704, 12810902, 12812812, 12820109, 12820307, 12820406, 12820505, 12820604, 12820703, 12820901, 12830207, 12830306, 12830405, 12830504, 12830603, 12830702, 12840107, 12840206, 12840305, 12840404, 12840503, 12840602, 12840701, 12850106, 12850205, 12850304, 12850403, 12850502, 12850601, 12860105, 12860204, 12860303, 12860402, 12860501, 12870104, 12870203, 12870302, 12870401, 12890102, 12890201, 13011824, 13012825, 13013826, 13014827, 13016829, 13018509, 13018707, 13018905, 13019832, 13021834, 13022835, 13023836, 13024837, 13026839, 13028609, 13028906, 13029842, 13031844, 13032845, 13033846, 13034847, 13036849, 13038709, 13038907, 13039852, 13041854, 13042855, 13043856, 13044857, 13046859, 13049862, 13051864, 13052865, 13053866, 13054867, 13056869, 13058909, 13059872, 13061874, 13062875, 13063876, 13064877, 13066879, 13079892, 13810309, 13810507, 13810606, 13810705, 13810903, 13813813, 13820209, 13820407, 13820506, 13820605, 13820704, 13820902, 13830109, 13830307, 13830406, 13830505, 13830604, 13830703, 13830901, 13840207, 13840306, 13840405, 13840504, 13840603, 13840702, 13850107, 13850206, 13850305, 13850404, 13850503, 13850602, 13850701, 13860106, 13860205, 13860304, 13860403, 13860502, 13860601, 13870105, 13870204, 13870303, 13870402, 13870501, 13890103, 13890202, 13890301, 14011825, 14012826, 14013827, 14015829, 14017831, 14018609, 14018906, 14019833, 14021835, 14022836, 14023837, 14025839, 14027841, 14028709, 14028907, 14029843, 14031845, 14032846, 14033847, 14035849, 14037851, 14039853, 14041855, 14042856, 14043857, 14045859, 14047861, 14048909, 14049863, 14051865, 14052866, 14053867, 14055869, 14057871, 14059873, 14061875, 14062876, 14063877, 14065879, 14077891, 14079893, 14810409, 14810607, 14810706, 14810904, 14814814, 14820309, 14820507, 14820606, 14820705, 14820903, 14830209, 14830407, 14830506, 14830605, 14830704, 14830902, 14840109, 14840307, 14840406, 14840505, 14840604, 14840703, 14840901, 14850207, 14850306, 14850405, 14850504, 14850603, 14850702, 14860107, 14860206, 14860305, 14860404, 14860503, 14860602, 14860701, 14870106, 14870205, 14870304, 14870403, 14870502, 14870601, 14890104, 14890203, 14890302, 14890401, 15011826, 15012827, 15014829, 15016831, 15017832, 15018709, 15018907, 15019834, 15021836, 15022837, 15024839, 15026841, 15027842, 15029844, 15031846, 15032847, 15034849, 15036851, 15037852, 15038909, 15039854, 15041856, 15042857, 15044859, 15046861, 15047862, 15049864, 15051866, 15052867, 15054869, 15056871, 15057872, 15059874, 15061876, 15062877, 15064879, 15076891, 15077892, 15079894, 15810509, 15810707, 15810905, 15815815, 15820409, 15820607, 15820706, 15820904, 15830309, 15830507, 15830606, 15830705, 15830903, 15840209, 15840407, 15840506, 15840605, 15840704, 15840902, 15850109, 15850307, 15850406, 15850505, 15850604, 15850703, 15850901, 15860207, 15860306, 15860405, 15860504, 15860603, 15860702, 15870107, 15870206, 15870305, 15870404, 15870503, 15870602, 15870701, 15890105, 15890204, 15890303, 15890402, 15890501, 16011827, 16013829, 16015831, 16016832, 16017833, 16019835, 16021837, 16023839, 16025841, 16026842, 16027843, 16028909, 16029845, 16031847, 16033849, 16035851, 16036852, 16037853, 16039855, 16041857, 16043859, 16045861, 16046862, 16047863, 16049865, 16051867, 16053869, 16055871, 16056872, 16057873, 16059875, 16061877, 16063879, 16075891, 16076892, 16077893, 16079895, 16810609, 16810906, 16816816, 16820509, 16820707, 16820905, 16830409, 16830607, 16830706, 16830904, 16840309, 16840507, 16840606, 16840705, 16840903, 16850209, 16850407, 16850506, 16850605, 16850704, 16850902, 16860109, 16860307, 16860406, 16860505, 16860604, 16860703, 16860901, 16870207, 16870306, 16870405, 16870504, 16870603, 16870702, 16890106, 16890205, 16890304, 16890403, 16890502, 16890601, 17012829, 17014831, 17015832, 17016833, 17017834, 17018909, 17019836, 17022839, 17024841, 17025842, 17026843, 17027844, 17029846, 17032849, 17034851, 17035852, 17036853, 17037854, 17039856, 17042859, 17044861, 17045862, 17046863, 17047864, 17049866, 17052869, 17054871, 17055872, 17056873, 17057874, 17059876, 17062879, 17074891, 17075892, 17076893, 17077894, 17079896, 17810709, 17810907, 17817817, 17820609, 17820906, 17830509, 17830707, 17830905, 17840409, 17840607, 17840706, 17840904, 17850309, 17850507, 17850606, 17850705, 17850903, 17860209, 17860407, 17860506, 17860605, 17860704, 17860902, 17870109, 17870307, 17870406, 17870505, 17870604, 17870703, 17870901, 17890107, 17890206, 17890305, 17890404, 17890503, 17890602, 17890701, 19012831, 19013832, 19014833, 19015834, 19016835, 19017836, 19022841, 19023842, 19024843, 19025844, 19026845, 19027846, 19032851, 19033852, 19034853, 19035854, 19036855, 19037856, 19042861, 19043862, 19044863, 19045864, 19046865, 19047866, 19052871, 19053872, 19054873, 19055874, 19056875, 19057876, 19072891, 19073892, 19074893, 19075894, 19076895, 19077896, 19810909, 19819819, 19830709, 19830907, 19840609, 19840906, 19850509, 19850707, 19850905, 19860409, 19860607, 19860706, 19860904, 19870309, 19870507, 19870606, 19870705, 19870903, 19890109, 19890307, 19890406, 19890505, 19890604, 19890703, 19890901, 20109812, 20118409, 20118607, 20118706, 20118904, 20128509, 20128707, 20128905, 20138609, 20138906, 20148709, 20148907, 20168909, 20207811, 20209813, 20306811, 20307812, 20309814, 20405811, 20406812, 20407813, 20409815, 20504811, 20505812, 20506813, 20507814, 20509816, 20603811, 20604812, 20605813, 20606814, 20607815, 20609817, 20702811, 20703812, 20704813, 20705814, 20706815, 20707816, 20901812, 20902813, 20903814, 20904815, 20905816, 20906817, 21011832, 21012833, 21013834, 21014835, 21015836, 21016837, 21021842, 21022843, 21023844, 21024845, 21025846, 21026847, 21031852, 21032853, 21033854, 21034855, 21035856, 21036857, 21041862, 21042863, 21043864, 21044865, 21045866, 21046867, 21051872, 21052873, 21053874, 21054875, 21055876, 21056877, 21071892, 21072893, 21073894, 21074895, 21075896, 21076897, 21821821, 21830909, 21850709, 21850907, 21860609, 21860906, 21870509, 21870707, 21870905, 21890309, 21890507, 21890606, 21890705, 21890903, 22011833, 22012834, 22013835, 22014836, 22015837, 22017839, 22019841, 22021843, 22022844, 22023845, 22024846, 22025847, 22027849, 22029851, 22031853, 22032854, 22033855, 22034856, 22035857, 22037859, 22039861, 22041863, 22042864, 22043865, 22044866, 22045867, 22047869, 22049871, 22051873, 22052874, 22053875, 22054876, 22055877, 22057879, 22069891, 22071893, 22072894, 22073895, 22074896, 22075897, 22077899, 22811011, 22822822, 22840909, 22860709, 22860907, 22870609, 22870906, 22890409, 22890607, 22890706, 22890904, 23011834, 23012835, 23013836, 23014837, 23016839, 23019842, 23021844, 23022845, 23023846, 23024847, 23026849, 23029852, 23031854, 23032855, 23033856, 23034857, 23036859, 23039862, 23041864, 23042865, 23043866, 23044867, 23046869, 23049872, 23051874, 23052875, 23053876, 23054877, 23056879, 23069892, 23071894, 23072895, 23073896, 23074897, 23076899, 23811012, 23812011, 23823823, 23850909, 23870709, 23870907, 23890509, 23890707, 23890905, 24011835, 24012836, 24013837, 24015839, 24017841, 24019843, 24021845, 24022846, 24023847, 24025849, 24027851, 24029853, 24031855, 24032856, 24033857, 24035859, 24037861, 24039863, 24041865, 24042866, 24043867, 24045869, 24047871, 24049873, 24051875, 24052876, 24053877, 24055879, 24067891, 24069893, 24071895, 24072896, 24073897, 24075899, 24811013, 24812012, 24813011, 24824824, 24860909, 24890609, 24890906, 25011836, 25012837, 25014839, 25016841, 25017842, 25019844, 25021846, 25022847, 25024849, 25026851, 25027852, 25029854, 25031856, 25032857, 25034859, 25036861, 25037862, 25039864, 25041866, 25042867, 25044869, 25046871, 25047872, 25049874, 25051876, 25052877, 25054879, 25066891, 25067892, 25069894, 25071896, 25072897, 25074899, 25811014, 25812013, 25813012, 25814011, 25825825, 25870909, 25890709, 25890907, 26011837, 26013839, 26015841, 26016842, 26017843, 26019845, 26021847, 26023849, 26025851, 26026852, 26027853, 26029855, 26031857, 26033859, 26035861, 26036862, 26037863, 26039865, 26041867, 26043869, 26045871, 26046872, 26047873, 26049875, 26051877, 26053879, 26065891, 26066892, 26067893, 26069895, 26071897, 26073899, 26811015, 26812014, 26813013, 26814012, 26815011, 26826826, 27012839, 27014841, 27015842, 27016843, 27017844, 27019846, 27022849, 27024851, 27025852, 27026853, 27027854, 27029856, 27032859, 27034861, 27035862, 27036863, 27037864, 27039866, 27042869, 27044871, 27045872, 27046873, 27047874, 27049876, 27052879, 27064891, 27065892, 27066893, 27067894, 27069896, 27072899, 27811016, 27812015, 27813014, 27814013, 27815012, 27816011, 27827827, 27890909, 29012841, 29013842, 29014843, 29015844, 29016845, 29017846, 29022851, 29023852, 29024853, 29025854, 29026855, 29027856, 29032861, 29033862, 29034863, 29035864, 29036865, 29037866, 29042871, 29043872, 29044873, 29045874, 29046875, 29047876, 29062891, 29063892, 29064893, 29065894, 29066895, 29067896, 29812017, 29813016, 29814015, 29815014, 29816013, 29817012, 29829829, 30107811, 30109813, 30118509, 30118707, 30118905, 30128609, 30128906, 30138709, 30138907, 30158909, 30206811, 30207812, 30209814, 30305811, 30306812, 30307813, 30309815, 30404811, 30405812, 30406813, 30407814, 30409816, 30503811, 30504812, 30505813, 30506814, 30507815, 30509817, 30602811, 30603812, 30604813, 30605814, 30606815, 30607816, 30701811, 30702812, 30703813, 30704814, 30705815, 30706816, 30707817, 30709819, 30901813, 30902814, 30903815, 30904816, 30905817, 30907819, 30909821, 30981011, 30981101, 31011842, 31012843, 31013844, 31014845, 31015846, 31016847, 31021852, 31022853, 31023854, 31024855, 31025856, 31026857, 31031862, 31032863, 31033864, 31034865, 31035866, 31036867, 31041872, 31042873, 31043874, 31044875, 31045876, 31046877, 31061892, 31062893, 31063894, 31064895, 31065896, 31066897, 31812019, 31814017, 31815016, 31816015, 31817014, 31819012, 31831831, 32011843, 32012844, 32013845, 32014846, 32015847, 32017849, 32019851, 32021853, 32022854, 32023855, 32024856, 32025857, 32027859, 32029861, 32031863, 32032864, 32033865, 32034866, 32035867, 32037869, 32039871, 32041873, 32042874, 32043875, 32044876, 32045877, 32047879, 32059891, 32061893, 32062894, 32063895, 32064896, 32065897, 32067899, 32811021, 32813019, 32815017, 32816016, 32817015, 32819013, 32821011, 32832832, 33011844, 33012845, 33013846, 33014847, 33016849, 33019852, 33021854, 33022855, 33023856, 33024857, 33026859, 33029862, 33031864, 33032865, 33033866, 33034867, 33036869, 33039872, 33041874, 33042875, 33043876, 33044877, 33046879, 33059892, 33061894, 33062895, 33063896, 33064897, 33066899, 33811022, 33812021, 33814019, 33816017, 33817016, 33819014, 33821012, 33822011, 33833833, 34011845, 34012846, 34013847, 34015849, 34017851, 34019853, 34021855, 34022856, 34023857, 34025859, 34027861, 34029863, 34031865, 34032866, 34033867, 34035869, 34037871, 34039873, 34041875, 34042876, 34043877, 34045879, 34057891, 34059893, 34061895, 34062896, 34063897, 34065899, 34811023, 34812022, 34813021, 34815019, 34817017, 34819015, 34821013, 34822012, 34823011, 34834834, 35011846, 35012847, 35014849, 35016851, 35017852, 35019854, 35021856, 35022857, 35024859, 35026861, 35027862, 35029864, 35031866, 35032867, 35034869, 35036871, 35037872, 35039874, 35041876, 35042877, 35044879, 35056891, 35057892, 35059894, 35061896, 35062897, 35064899, 35811024, 35812023, 35813022, 35814021, 35816019, 35819016, 35821014, 35822013, 35823012, 35824011, 35835835, 36011847, 36013849, 36015851, 36016852, 36017853, 36019855, 36021857, 36023859, 36025861, 36026862, 36027863, 36029865, 36031867, 36033869, 36035871, 36036872, 36037873, 36039875, 36041877, 36043879, 36055891, 36056892, 36057893, 36059895, 36061897, 36063899, 36811025, 36812024, 36813023, 36814022, 36815021, 36817019, 36819017, 36821015, 36822014, 36823013, 36824012, 36825011, 36836836, 37012849, 37014851, 37015852, 37016853, 37017854, 37019856, 37022859, 37024861, 37025862, 37026863, 37027864, 37029866, 37032869, 37034871, 37035872, 37036873, 37037874, 37039876, 37042879, 37054891, 37055892, 37056893, 37057894, 37059896, 37062899, 37811026, 37812025, 37813024, 37814023, 37815022, 37816021, 37821016, 37822015, 37823014, 37824013, 37825012, 37826011, 37837837, 39012851, 39013852, 39014853, 39015854, 39016855, 39017856, 39022861, 39023862, 39024863, 39025864, 39026865, 39027866, 39032871, 39033872, 39034873, 39035874, 39036875, 39037876, 39052891, 39053892, 39054893, 39055894, 39056895, 39057896, 39812027, 39813026, 39814025, 39815024, 39816023, 39817022, 39822017, 39823016, 39824015, 39825014, 39826013, 39827012, 39839839, 40106811, 40107812, 40109814, 40118609, 40118906, 40128709, 40128907, 40148909, 40205811, 40206812, 40207813, 40209815, 40304811, 40305812, 40306813, 40307814, 40309816, 40403811, 40404812, 40405813, 40406814, 40407815, 40409817, 40502811, 40503812, 40504813, 40505814, 40506815, 40507816, 40601811, 40602812, 40603813, 40604814, 40605815, 40606816, 40607817, 40609819, 40701812, 40702813, 40703814, 40704815, 40705816, 40706817, 40901814, 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94851043, 94852042, 94853041, 94855039, 94857037, 94859035, 94861033, 94862032, 94863031, 94865029, 94867027, 94869025, 94871023, 94872022, 94873021, 94875019, 94877017, 94879015, 94894894, 95816079, 95819076, 95821074, 95822073, 95823072, 95824071, 95826069, 95829066, 95831064, 95832063, 95833062, 95834061, 95836059, 95839056, 95841054, 95842053, 95843052, 95844051, 95846049, 95849046, 95851044, 95852043, 95853042, 95854041, 95856039, 95859036, 95861034, 95862033, 95863032, 95864031, 95866029, 95869026, 95871024, 95872023, 95873022, 95874021, 95876019, 95879016, 95895895, 96817079, 96819077, 96821075, 96822074, 96823073, 96824072, 96825071, 96827069, 96829067, 96831065, 96832064, 96833063, 96834062, 96835061, 96837059, 96839057, 96841055, 96842054, 96843053, 96844052, 96845051, 96847049, 96849047, 96851045, 96852044, 96853043, 96854042, 96855041, 96857039, 96859037, 96861035, 96862034, 96863033, 96864032, 96865031, 96867029, 96869027, 96871025, 96872024, 96873023, 96874022, 96875021, 96877019, 96879017, 96896896, 97821076, 97822075, 97823074, 97824073, 97825072, 97826071, 97831066, 97832065, 97833064, 97834063, 97835062, 97836061, 97841056, 97842055, 97843054, 97844053, 97845052, 97846051, 97851046, 97852045, 97853044, 97854043, 97855042, 97856041, 97861036, 97862035, 97863034, 97864033, 97865032, 97866031, 97871026, 97872025, 97873024, 97874023, 97875022, 97876021, 97897897, 99822077, 99823076, 99824075, 99825074, 99826073, 99827072, 99832067, 99833066, 99834065, 99835064, 99836063, 99837062, 99842057, 99843056, 99844055, 99845054, 99846053, 99847052, 99852047, 99853046, 99854045, 99855044, 99856043, 99857042, 99862037, 99863036, 99864035, 99865034, 99866033, 99867032, 99872027, 99873026, 99874025, 99875024, 99876023, 99877022, 99899899.

 

Note that for symmetry reasons the code [0=8+] would also produce a maximum of 3376 terms:

 

S’(8) = 11011011, 11018189, 11018387, 11018486, 11018585, 11018684, 11018783, 11018981, 11028287, 11028386, 11028485, 11028584, 11028683, 11028782, 11038187, 11038286, 11038385, 11038484, 11038583, 11038682, 11038781, 11048186, 11048285, 11048384, 11048483, 11048582, 11048681, 11058185, 11058284, 11058383, 11058482, 11058581, 11068184, 11068283, 11068382, 11068481, 11078183, 11078282, 11078381, 11098181, 11810389, 11810587, 11810686, 11810785, 11810983, 11811022, 11812023, 11813024, 11814025, 11815026, 11816027, 11820489, 11820687, 11820786, 11820984, 11821032, 11822033, 11823034, 11824035, 11825036, 11826037, 11830589, 11830787, 11830985, 11831042, 11832043, 11833044, 11834045, 11835046, 11836047, 11840689, 11840986, 11841052, 11842053, 11843054, 11844055, 11845056, 11846057, 11850789, 11850987, 11851062, 11852063, 11853064, 11854065, 11855066, 11856067, 11861072, 11862073, 11863074, 11864075, 11865076, 11866077, 11870989, 12012012, 12018289, 12018487, 12018586, 12018685, 12018784, 12018982, 12028189, 12028387, 12028486, 12028585, 12028684, 12028783, 12028981, 12038287, 12038386, 12038485, 12038584, 12038683, 12038782, 12048187, 12048286, 12048385, 12048484, 12048583, 12048682, 12048781, 12058186, 12058285, 12058384, 12058483, 12058582, 12058681, 12068185, 12068284, 12068383, 12068482, 12068581, 12078184, 12078283, 12078382, 12078481, 12098182, 12098281, 12810489, 12810687, 12810786, 12810984, 12811023, 12812024, 12813025, 12814026, 12815027, 12817029, 12819031, 12820589, 12820787, 12820985, 12821033, 12822034, 12823035, 12824036, 12825037, 12827039, 12829041, 12830689, 12830986, 12831043, 12832044, 12833045, 12834046, 12835047, 12837049, 12839051, 12840789, 12840987, 12841053, 12842054, 12843055, 12844056, 12845057, 12847059, 12849061, 12851063, 12852064, 12853065, 12854066, 12855067, 12857069, 12859071, 12860989, 12861073, 12862074, 12863075, 12864076, 12865077, 12867079, 12879091, 13013013, 13018389, 13018587, 13018686, 13018785, 13018983, 13028289, 13028487, 13028586, 13028685, 13028784, 13028982, 13038189, 13038387, 13038486, 13038585, 13038684, 13038783, 13038981, 13048287, 13048386, 13048485, 13048584, 13048683, 13048782, 13058187, 13058286, 13058385, 13058484, 13058583, 13058682, 13058781, 13068186, 13068285, 13068384, 13068483, 13068582, 13068681, 13078185, 13078284, 13078383, 13078482, 13078581, 13098183, 13098282, 13098381, 13810589, 13810787, 13810985, 13811024, 13812025, 13813026, 13814027, 13816029, 13819032, 13820689, 13820986, 13821034, 13822035, 13823036, 13824037, 13826039, 13829042, 13830789, 13830987, 13831044, 13832045, 13833046, 13834047, 13836049, 13839052, 13841054, 13842055, 13843056, 13844057, 13846059, 13849062, 13850989, 13851064, 13852065, 13853066, 13854067, 13856069, 13859072, 13861074, 13862075, 13863076, 13864077, 13866079, 13879092, 14014014, 14018489, 14018687, 14018786, 14018984, 14028389, 14028587, 14028686, 14028785, 14028983, 14038289, 14038487, 14038586, 14038685, 14038784, 14038982, 14048189, 14048387, 14048486, 14048585, 14048684, 14048783, 14048981, 14058287, 14058386, 14058485, 14058584, 14058683, 14058782, 14068187, 14068286, 14068385, 14068484, 14068583, 14068682, 14068781, 14078186, 14078285, 14078384, 14078483, 14078582, 14078681, 14098184, 14098283, 14098382, 14098481, 14810689, 14810986, 14811025, 14812026, 14813027, 14815029, 14817031, 14819033, 14820789, 14820987, 14821035, 14822036, 14823037, 14825039, 14827041, 14829043, 14831045, 14832046, 14833047, 14835049, 14837051, 14839053, 14840989, 14841055, 14842056, 14843057, 14845059, 14847061, 14849063, 14851065, 14852066, 14853067, 14855069, 14857071, 14859073, 14861075, 14862076, 14863077, 14865079, 14877091, 14879093, 15015015, 15018589, 15018787, 15018985, 15028489, 15028687, 15028786, 15028984, 15038389, 15038587, 15038686, 15038785, 15038983, 15048289, 15048487, 15048586, 15048685, 15048784, 15048982, 15058189, 15058387, 15058486, 15058585, 15058684, 15058783, 15058981, 15068287, 15068386, 15068485, 15068584, 15068683, 15068782, 15078187, 15078286, 15078385, 15078484, 15078583, 15078682, 15078781, 15098185, 15098284, 15098383, 15098482, 15098581, 15810789, 15810987, 15811026, 15812027, 15814029, 15816031, 15817032, 15819034, 15821036, 15822037, 15824039, 15826041, 15827042, 15829044, 15830989, 15831046, 15832047, 15834049, 15836051, 15837052, 15839054, 15841056, 15842057, 15844059, 15846061, 15847062, 15849064, 15851066, 15852067, 15854069, 15856071, 15857072, 15859074, 15861076, 15862077, 15864079, 15876091, 15877092, 15879094, 16016016, 16018689, 16018986, 16028589, 16028787, 16028985, 16038489, 16038687, 16038786, 16038984, 16048389, 16048587, 16048686, 16048785, 16048983, 16058289, 16058487, 16058586, 16058685, 16058784, 16058982, 16068189, 16068387, 16068486, 16068585, 16068684, 16068783, 16068981, 16078287, 16078386, 16078485, 16078584, 16078683, 16078782, 16098186, 16098285, 16098384, 16098483, 16098582, 16098681, 16811027, 16813029, 16815031, 16816032, 16817033, 16819035, 16820989, 16821037, 16823039, 16825041, 16826042, 16827043, 16829045, 16831047, 16833049, 16835051, 16836052, 16837053, 16839055, 16841057, 16843059, 16845061, 16846062, 16847063, 16849065, 16851067, 16853069, 16855071, 16856072, 16857073, 16859075, 16861077, 16863079, 16875091, 16876092, 16877093, 16879095, 17017017, 17018789, 17018987, 17028689, 17028986, 17038589, 17038787, 17038985, 17048489, 17048687, 17048786, 17048984, 17058389, 17058587, 17058686, 17058785, 17058983, 17068289, 17068487, 17068586, 17068685, 17068784, 17068982, 17078189, 17078387, 17078486, 17078585, 17078684, 17078783, 17078981, 17098187, 17098286, 17098385, 17098484, 17098583, 17098682, 17098781, 17810989, 17812029, 17814031, 17815032, 17816033, 17817034, 17819036, 17822039, 17824041, 17825042, 17826043, 17827044, 17829046, 17832049, 17834051, 17835052, 17836053, 17837054, 17839056, 17842059, 17844061, 17845062, 17846063, 17847064, 17849066, 17852069, 17854071, 17855072, 17856073, 17857074, 17859076, 17862079, 17874091, 17875092, 17876093, 17877094, 17879096, 18110389, 18110587, 18110686, 18110785, 18110983, 18120489, 18120687, 18120786, 18120984, 18130589, 18130787, 18130985, 18140689, 18140986, 18150789, 18150987, 18170989, 18189011, 18289012, 18387011, 18389013, 18486011, 18487012, 18489014, 18585011, 18586012, 18587013, 18589015, 18684011, 18685012, 18686013, 18687014, 18689016, 18783011, 18784012, 18785013, 18786014, 18787015, 18789017, 18981011, 18982012, 18983013, 18984014, 18985015, 18986016, 18987017, 18989019, 19018989, 19019019, 19038789, 19038987, 19048689, 19048986, 19058589, 19058787, 19058985, 19068489, 19068687, 19068786, 19068984, 19078389, 19078587, 19078686, 19078785, 19078983, 19098189, 19098387, 19098486, 19098585, 19098684, 19098783, 19098981, 19812031, 19813032, 19814033, 19815034, 19816035, 19817036, 19822041, 19823042, 19824043, 19825044, 19826045, 19827046, 19832051, 19833052, 19834053, 19835054, 19836055, 19837056, 19842061, 19843062, 19844063, 19845064, 19846065, 19847066, 19852071, 19853072, 19854073, 19855074, 19856075, 19857076, 19872091, 19873092, 19874093, 19875094, 19876095, 19877096, 21021021, 21038989, 21058789, 21058987, 21068689, 21068986, 21078589, 21078787, 21078985, 21098389, 21098587, 21098686, 21098785, 21098983, 21811032, 21812033, 21813034, 21814035, 21815036, 21816037, 21821042, 21822043, 21823044, 21824045, 21825046, 21826047, 21831052, 21832053, 21833054, 21834055, 21835056, 21836057, 21841062, 21842063, 21843064, 21844065, 21845066, 21846067, 21851072, 21852073, 21853074, 21854075, 21855076, 21856077, 21871092, 21872093, 21873094, 21874095, 21875096, 21876097, 22011811, 22022022, 22048989, 22068789, 22068987, 22078689, 22078986, 22098489, 22098687, 22098786, 22098984, 22811033, 22812034, 22813035, 22814036, 22815037, 22817039, 22819041, 22821043, 22822044, 22823045, 22824046, 22825047, 22827049, 22829051, 22831053, 22832054, 22833055, 22834056, 22835057, 22837059, 22839061, 22841063, 22842064, 22843065, 22844066, 22845067, 22847069, 22849071, 22851073, 22852074, 22853075, 22854076, 22855077, 22857079, 22869091, 22871093, 22872094, 22873095, 22874096, 22875097, 22877099, 23011812, 23012811, 23023023, 23058989, 23078789, 23078987, 23098589, 23098787, 23098985, 23811034, 23812035, 23813036, 23814037, 23816039, 23819042, 23821044, 23822045, 23823046, 23824047, 23826049, 23829052, 23831054, 23832055, 23833056, 23834057, 23836059, 23839062, 23841064, 23842065, 23843066, 23844067, 23846069, 23849072, 23851074, 23852075, 23853076, 23854077, 23856079, 23869092, 23871094, 23872095, 23873096, 23874097, 23876099, 24011813, 24012812, 24013811, 24024024, 24068989, 24098689, 24098986, 24811035, 24812036, 24813037, 24815039, 24817041, 24819043, 24821045, 24822046, 24823047, 24825049, 24827051, 24829053, 24831055, 24832056, 24833057, 24835059, 24837061, 24839063, 24841065, 24842066, 24843067, 24845069, 24847071, 24849073, 24851075, 24852076, 24853077, 24855079, 24867091, 24869093, 24871095, 24872096, 24873097, 24875099, 25011814, 25012813, 25013812, 25014811, 25025025, 25078989, 25098789, 25098987, 25811036, 25812037, 25814039, 25816041, 25817042, 25819044, 25821046, 25822047, 25824049, 25826051, 25827052, 25829054, 25831056, 25832057, 25834059, 25836061, 25837062, 25839064, 25841066, 25842067, 25844069, 25846071, 25847072, 25849074, 25851076, 25852077, 25854079, 25866091, 25867092, 25869094, 25871096, 25872097, 25874099, 26011815, 26012814, 26013813, 26014812, 26015811, 26026026, 26811037, 26813039, 26815041, 26816042, 26817043, 26819045, 26821047, 26823049, 26825051, 26826052, 26827053, 26829055, 26831057, 26833059, 26835061, 26836062, 26837063, 26839065, 26841067, 26843069, 26845071, 26846072, 26847073, 26849075, 26851077, 26853079, 26865091, 26866092, 26867093, 26869095, 26871097, 26873099, 27011816, 27012815, 27013814, 27014813, 27015812, 27016811, 27027027, 27098989, 27812039, 27814041, 27815042, 27816043, 27817044, 27819046, 27822049, 27824051, 27825052, 27826053, 27827054, 27829056, 27832059, 27834061, 27835062, 27836063, 27837064, 27839066, 27842069, 27844071, 27845072, 27846073, 27847074, 27849076, 27852079, 27864091, 27865092, 27866093, 27867094, 27869096, 27872099, 28110489, 28110687, 28110786, 28110984, 28120589, 28120787, 28120985, 28130689, 28130986, 28140789, 28140987, 28160989, 28189012, 28287011, 28289013, 28386011, 28387012, 28389014, 28485011, 28486012, 28487013, 28489015, 28584011, 28585012, 28586013, 28587014, 28589016, 28683011, 28684012, 28685013, 28686014, 28687015, 28689017, 28782011, 28783012, 28784013, 28785014, 28786015, 28787016, 28981012, 28982013, 28983014, 28984015, 28985016, 28986017, 29012817, 29013816, 29014815, 29015814, 29016813, 29017812, 29029029, 29812041, 29813042, 29814043, 29815044, 29816045, 29817046, 29822051, 29823052, 29824053, 29825054, 29826055, 29827056, 29832061, 29833062, 29834063, 29835064, 29836065, 29837066, 29842071, 29843072, 29844073, 29845074, 29846075, 29847076, 29862091, 29863092, 29864093, 29865094, 29866095, 29867096, 31012819, 31014817, 31015816, 31016815, 31017814, 31019812, 31031031, 31811042, 31812043, 31813044, 31814045, 31815046, 31816047, 31821052, 31822053, 31823054, 31824055, 31825056, 31826057, 31831062, 31832063, 31833064, 31834065, 31835066, 31836067, 31841072, 31842073, 31843074, 31844075, 31845076, 31846077, 31861092, 31862093, 31863094, 31864095, 31865096, 31866097, 32011821, 32013819, 32015817, 32016816, 32017815, 32019813, 32021811, 32032032, 32811043, 32812044, 32813045, 32814046, 32815047, 32817049, 32819051, 32821053, 32822054, 32823055, 32824056, 32825057, 32827059, 32829061, 32831063, 32832064, 32833065, 32834066, 32835067, 32837069, 32839071, 32841073, 32842074, 32843075, 32844076, 32845077, 32847079, 32859091, 32861093, 32862094, 32863095, 32864096, 32865097, 32867099, 33011822, 33012821, 33014819, 33016817, 33017816, 33019814, 33021812, 33022811, 33033033, 33811044, 33812045, 33813046, 33814047, 33816049, 33819052, 33821054, 33822055, 33823056, 33824057, 33826059, 33829062, 33831064, 33832065, 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94043851, 94045849, 94047847, 94049845, 94051843, 94052842, 94053841, 94055839, 94057837, 94059835, 94061833, 94062832, 94063831, 94065829, 94067827, 94069825, 94071823, 94072822, 94073821, 94075819, 94077817, 94079815, 94094094, 95016879, 95019876, 95021874, 95022873, 95023872, 95024871, 95026869, 95029866, 95031864, 95032863, 95033862, 95034861, 95036859, 95039856, 95041854, 95042853, 95043852, 95044851, 95046849, 95049846, 95051844, 95052843, 95053842, 95054841, 95056839, 95059836, 95061834, 95062833, 95063832, 95064831, 95066829, 95069826, 95071824, 95072823, 95073822, 95074821, 95076819, 95079816, 95095095, 96017879, 96019877, 96021875, 96022874, 96023873, 96024872, 96025871, 96027869, 96029867, 96031865, 96032864, 96033863, 96034862, 96035861, 96037859, 96039857, 96041855, 96042854, 96043853, 96044852, 96045851, 96047849, 96049847, 96051845, 96052844, 96053843, 96054842, 96055841, 96057839, 96059837, 96061835, 96062834, 96063833, 96064832, 96065831, 96067829, 96069827, 96071825, 96072824, 96073823, 96074822, 96075821, 96077819, 96079817, 96096096, 97021876, 97022875, 97023874, 97024873, 97025872, 97026871, 97031866, 97032865, 97033864, 97034863, 97035862, 97036861, 97041856, 97042855, 97043854, 97044853, 97045852, 97046851, 97051846, 97052845, 97053844, 97054843, 97055842, 97056841, 97061836, 97062835, 97063834, 97064833, 97065832, 97066831, 97071826, 97072825, 97073824, 97074823, 97075822, 97076821, 97097097, 98181011, 98182012, 98183013, 98184014, 98185015, 98186016, 98187017, 98189019, 98281012, 98282013, 98283014, 98284015, 98285016, 98286017, 98301181, 98301811, 98381013, 98382014, 98383015, 98384016, 98385017, 98387019, 98389021, 98401182, 98401281, 98401812, 98402811, 98481014, 98482015, 98483016, 98484017, 98486019, 98489022, 98501183, 98501282, 98501381, 98501813, 98502812, 98503811, 98581015, 98582016, 98583017, 98585019, 98587021, 98589023, 98601184, 98601283, 98601382, 98601481, 98601814, 98602813, 98603812, 98604811, 98681016, 98682017, 98684019, 98686021, 98687022, 98689024, 98701185, 98701284, 98701383, 98701482, 98701581, 98701815, 98702814, 98703813, 98704812, 98705811, 98781017, 98783019, 98785021, 98786022, 98787023, 98789025, 98901187, 98901286, 98901385, 98901484, 98901583, 98901682, 98901781, 98901817, 98902816, 98903815, 98904814, 98905813, 98906812, 98907811, 98981019, 98983021, 98984022, 98985023, 98986024, 98987025, 98989027, 99022877, 99023876, 99024875, 99025874, 99026873, 99027872, 99032867, 99033866, 99034865, 99035864, 99036863, 99037862, 99042857, 99043856, 99044855, 99045854, 99046853, 99047852, 99052847, 99053846, 99054845, 99055844, 99056843, 99057842, 99062837, 99063836, 99064835, 99065834, 99066833, 99067832, 99072827, 99073826, 99074825, 99075824, 99076823, 99077822, 99099099,

 

Thanks, Hans, beautiful!

Best,

É.

 

(back to main page)

 

(or try to solve this, which was sent on Feb. 10th, 2009 at 15:08 to Rec.Puzzles and never answered by anyone!)

 

(corrected version without typo)

 

Hello Rec.Puzzlers,

 

Let's pretend I was born the 29 of August 1951;

write this the usual administrative way [yyyymmdd]: 19510829

If we substitute + to 5 and = to 8 we would have:   19+10=29

... which is arithmetically true.

Let's note the above substitution [5+;8=]

 

To be born the 29 of March 1971 would produce  ->  ->  19710329

If we substitue + to 7 and = to 3 we would have again: 19+10=29

The substitution is now [7+;3=]

 

To be born the 29 of January 1981 would produce 19810129

No substitution can turn this into a sound equation.

For instance [8+;1=] would give =9+=0=29

                                19810129

 

To be born the 8 of December 1961 would produce 19611208

If we apply [2+;6=] we would have  ->  ->  ->   19=11+08

... which we admit as being true (despite the leading zero of 08)

 

a) What are all the "good" birthday dates with the substitution [a+;b=]

b) Same question with [a-;b=]

c) Same question with [a*;b=]

d) Same question with [a/;b=]

 

(If both birthday dates of you and your partner/lover/wife/boyfriend

etc. share the same substitution, please let us know!)

;-)

Best,

Éric A. (eric tod angelini ta skynet tod be) <- cleverly scrambled, uh!

 

__________

 

Last minute:

Hans has just sent (Feb. 11, 2009) a “little bonus”: enjoy!

 

Number of 9-digit solutions:

 

=\+      0       1       2       3       4       5       6       7       8

 

1        -

2        -       -

3        -       -       -

4        -       -       -       -

5        -       -       -       -       -

6        -       -       -       -       -       -

7    49673       -       -       -       -       -       -

8    50112       -       -       -       -       -       -       -

9    53219       -       -       -       -       -       -       -       -

 

Probable maximum (53219): see table here.