Chris Hartman (![[info]](http://p-stat.livejournal.com/img/userinfo.gif){kind=small} chrishartman) wrote,@ 2006-03-23 16:55:00 |
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Wasting time on puzzles...
captaino posts some interesting math puzzles. In puzzle #10, he asks for a number where multiplying by 7 moves a 7 from the end to the beginning. (A short example with 4 is 4*102564=410256). I wasted hours solving it (see the comments). Then, in a free moment today, I wrote a program to generate all the answers for all single digits in all bases up to 16. The results are behind the cut.
In base 3 try 1*1
In base 3 try 2*1012
In base 4 try 1*1
In base 4 try 2*102
In base 4 try 3*10113
In base 5 try 1*1
In base 5 try 2*102342
In base 5 try 3*101343
In base 5 try 4*101124214
In base 6 try 1*1
In base 6 try 2*1031345242
In base 6 try 3*1020412245351433
In base 6 try 4*10132203044
In base 6 try 5*10112404544315
In base 7 try 1*1
In base 7 try 2*103524563142
In base 7 try 3*1023
In base 7 try 4*101546324
In base 7 try 5*1013042156536245
In base 7 try 6*10112363262135202250565543034045314644
In base 8 try 1*1
In base 8 try 2*1042
In base 8 try 3*10262054413
In base 8 try 4*10204
In base 8 try 5*1015
In base 8 try 6*10127114202562304053446
In base 8 try 7*10112362022474404517
In base 9 try 1*1
In base 9 try 2*10467842
In base 9 try 3*103
In base 9 try 4*102274
In base 9 try 5*10175
In base 9 try 6*10146711624827874217726406
In base 9 try 7*101267355850647
In base 9 try 8*10112360675404505630337202247314618
In base 10 try 1*1
In base 10 try 2*105263157894736842
In base 10 try 3*1034482758620689655172413793
In base 10 try 4*102564
In base 10 try 5*10204081632653061224489795918367346938
In base 10 try 6*10169491525423728813559322033898305084
In base 10 try 7*1014492753623188405797
In base 10 try 8*1012658227848
In base 10 try 9*10112359550561797752808988764044943820
In base 11 try 1*1
In base 11 try 2*105842
In base 11 try 3*10386593
In base 11 try 4*1028a54
In base 11 try 5*1022714759a8839635
In base 11 try 6*101952786a36
In base 11 try 7*101657
In base 11 try 8*10143318520286635a4056217098
In base 11 try 9*10126441757a732895a49
In base 11 try a*101123594269539202247078527a7740449314
In base 12 try 1*1
In base 12 try 2*10631694842
In base 12 try 3*10414559b393
In base 12 try 4*10309236a88206164719544
In base 12 try 5*1025355a9433073a458409919b715
In base 12 try 6*1020408142854a997732650a18346916306
In base 12 try 7*101899b864406b33aa15423913745949305255
In base 12 try 8*10162334b148
In base 12 try 9*101419648634459b9384b26b533040547216a1
In base 12 try a*101263037690aa832880982025060731619946
In base 12 try b*1011235930336a53909a873b325819b9975055
In base 13 try 1*1
In base 13 try 2*1069b5948abc63173842
In base 13 try 3*1045a7b39bc8725193
In base 13 try 4*1034
In base 13 try 5*1028435b7691a9c5
In base 13 try 6*10226bcaa6
In base 13 try 7*101b546298a7
In base 13 try 8*101843a2b979119c8
In base 13 try 9*1015c2a5650739
In base 13 try a*101405317c65aca4c269a
In base 13 try b*10126197c70843c239a464173037552ab81bcb
In base 13 try c*101123591acaa861794044909a74c437b64b31
In base 14 try 1*1
In base 14 try 2*10738b59bcd6a52842
In base 14 try 3*104acd93
In base 14 try 4*1037c68924
In base 14 try 5*102baa79d28cdb233640b5
In base 14 try 6*10250bb43071275c91737839d47a8ab1bd93c4
In base 14 try 7*102040812244893468d3c7b183264c9b58b387
In base 14 try 8*101aa1392c88
In base 14 try 9*1017d484063b4521b13368724cdc60959d7a29
In base 14 try a*1015a534764b97d577a80b3cdc838a96792460
In base 14 try b*1013d1292166d506595d3a746ab24051a4a885
In base 14 try c*10126070830374171a90a7c4753d2398d81bb6
In base 14 try d*1011235909a628b639d995055b30336a2d2134
In base 15 try 1*1
In base 15 try 2*107b5a528bd6acde73949c631842
In base 15 try 3*1051a87c93
In base 15 try 4*103c30b69244c6ce758d71ba65514
In base 15 try 5*103091c571643cb849debe5d297d8ab236a5
In base 15 try 6*1027dc483d22ce9e255d73a940a1a433078b6d
In base 15 try 7*10226ba39147
In base 15 try 8*101d5648
In base 15 try 9*101a2be9e69
In base 15 try a*10179b72334c73ad1496e2dbd2c4365203047e
In base 15 try b*10158a506cd6a244735b6761dc270990c53304
In base 15 try c*1013cc4b9ac23e128e76d1151a21657e6303b8
In base 15 try d*10125e48663e23979c46195505beb7c214ab32
In base 15 try e*10112358e8819b628b5167e76e65c30336a1bd
In base 16 try 1*1
In base 16 try 2*10842
In base 16 try 3*10572620ae4c415c9882b93
In base 16 try 4*104
In base 16 try 5*1033d91d2a2067b23a5440cf6474a8819ec8e9
In base 16 try 6*102b1da46
In base 16 try 7*1024e6a17
In base 16 try 8*1020408
In base 16 try 9*101ca4b3055ee19
In base 16 try a*1019c2d14ee4a
In base 16 try b*101767dce434a9b
In base 16 try c*101571ed3c506b39a22d9218202ae3da78a0d6
In base 16 try d*1013c995a47babe74404f265691eeaf9d
In base 16 try e*10125e22708092f113840497889c2024bc44e
In base 16 try f*10112358e75d30336a0ab617909a3e202246b1
captaino posts some interesting math puzzles. In puzzle #10, he asks for a number where multiplying by 7 moves a 7 from the end to the beginning. (A short example with 4 is 4*102564=410256). I wasted hours solving it (see the comments). Then, in a free moment today, I wrote a program to generate all the answers for all single digits in all bases up to 16. The results are behind the cut.In base 3 try 1*1
In base 3 try 2*1012
In base 4 try 1*1
In base 4 try 2*102
In base 4 try 3*10113
In base 5 try 1*1
In base 5 try 2*102342
In base 5 try 3*101343
In base 5 try 4*101124214
In base 6 try 1*1
In base 6 try 2*1031345242
In base 6 try 3*1020412245351433
In base 6 try 4*10132203044
In base 6 try 5*10112404544315
In base 7 try 1*1
In base 7 try 2*103524563142
In base 7 try 3*1023
In base 7 try 4*101546324
In base 7 try 5*1013042156536245
In base 7 try 6*10112363262135202250565543034045314644
In base 8 try 1*1
In base 8 try 2*1042
In base 8 try 3*10262054413
In base 8 try 4*10204
In base 8 try 5*1015
In base 8 try 6*10127114202562304053446
In base 8 try 7*10112362022474404517
In base 9 try 1*1
In base 9 try 2*10467842
In base 9 try 3*103
In base 9 try 4*102274
In base 9 try 5*10175
In base 9 try 6*10146711624827874217726406
In base 9 try 7*101267355850647
In base 9 try 8*10112360675404505630337202247314618
In base 10 try 1*1
In base 10 try 2*105263157894736842
In base 10 try 3*1034482758620689655172413793
In base 10 try 4*102564
In base 10 try 5*10204081632653061224489795918367346938
In base 10 try 6*10169491525423728813559322033898305084
In base 10 try 7*1014492753623188405797
In base 10 try 8*1012658227848
In base 10 try 9*10112359550561797752808988764044943820
In base 11 try 1*1
In base 11 try 2*105842
In base 11 try 3*10386593
In base 11 try 4*1028a54
In base 11 try 5*1022714759a8839635
In base 11 try 6*101952786a36
In base 11 try 7*101657
In base 11 try 8*10143318520286635a4056217098
In base 11 try 9*10126441757a732895a49
In base 11 try a*101123594269539202247078527a7740449314
In base 12 try 1*1
In base 12 try 2*10631694842
In base 12 try 3*10414559b393
In base 12 try 4*10309236a88206164719544
In base 12 try 5*1025355a9433073a458409919b715
In base 12 try 6*1020408142854a997732650a18346916306
In base 12 try 7*101899b864406b33aa15423913745949305255
In base 12 try 8*10162334b148
In base 12 try 9*101419648634459b9384b26b533040547216a1
In base 12 try a*101263037690aa832880982025060731619946
In base 12 try b*1011235930336a53909a873b325819b9975055
In base 13 try 1*1
In base 13 try 2*1069b5948abc63173842
In base 13 try 3*1045a7b39bc8725193
In base 13 try 4*1034
In base 13 try 5*1028435b7691a9c5
In base 13 try 6*10226bcaa6
In base 13 try 7*101b546298a7
In base 13 try 8*101843a2b979119c8
In base 13 try 9*1015c2a5650739
In base 13 try a*101405317c65aca4c269a
In base 13 try b*10126197c70843c239a464173037552ab81bcb
In base 13 try c*101123591acaa861794044909a74c437b64b31
In base 14 try 1*1
In base 14 try 2*10738b59bcd6a52842
In base 14 try 3*104acd93
In base 14 try 4*1037c68924
In base 14 try 5*102baa79d28cdb233640b5
In base 14 try 6*10250bb43071275c91737839d47a8ab1bd93c4
In base 14 try 7*102040812244893468d3c7b183264c9b58b387
In base 14 try 8*101aa1392c88
In base 14 try 9*1017d484063b4521b13368724cdc60959d7a29
In base 14 try a*1015a534764b97d577a80b3cdc838a96792460
In base 14 try b*1013d1292166d506595d3a746ab24051a4a885
In base 14 try c*10126070830374171a90a7c4753d2398d81bb6
In base 14 try d*1011235909a628b639d995055b30336a2d2134
In base 15 try 1*1
In base 15 try 2*107b5a528bd6acde73949c631842
In base 15 try 3*1051a87c93
In base 15 try 4*103c30b69244c6ce758d71ba65514
In base 15 try 5*103091c571643cb849debe5d297d8ab236a5
In base 15 try 6*1027dc483d22ce9e255d73a940a1a433078b6d
In base 15 try 7*10226ba39147
In base 15 try 8*101d5648
In base 15 try 9*101a2be9e69
In base 15 try a*10179b72334c73ad1496e2dbd2c4365203047e
In base 15 try b*10158a506cd6a244735b6761dc270990c53304
In base 15 try c*1013cc4b9ac23e128e76d1151a21657e6303b8
In base 15 try d*10125e48663e23979c46195505beb7c214ab32
In base 15 try e*10112358e8819b628b5167e76e65c30336a1bd
In base 16 try 1*1
In base 16 try 2*10842
In base 16 try 3*10572620ae4c415c9882b93
In base 16 try 4*104
In base 16 try 5*1033d91d2a2067b23a5440cf6474a8819ec8e9
In base 16 try 6*102b1da46
In base 16 try 7*1024e6a17
In base 16 try 8*1020408
In base 16 try 9*101ca4b3055ee19
In base 16 try a*1019c2d14ee4a
In base 16 try b*101767dce434a9b
In base 16 try c*101571ed3c506b39a22d9218202ae3da78a0d6
In base 16 try d*1013c995a47babe74404f265691eeaf9d
In base 16 try e*10125e22708092f113840497889c2024bc44e
In base 16 try f*10112358e75d30336a0ab617909a3e202246b1
