Problems & Puzzles: Puzzles

 Puzzle 667 Puzzle 77 This puzzle has received one solution in 1999 a better one in 2009 and no more after that. Perhaps it's time to get one more solution now. After all it's almost christmas! Q. Improve the solutions to Puzzle 77

Contributions came from Seiji Tomita and Jan van Delden

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Seiji wrote:

Q3:

Solutions for R=7, only bottom rows.

Ending digit 1: 3631 2731 991 2251 11311 8011 11551, Total=149278
Ending digit 3: 823 463 2503 1663 9463 2383 8263, Total=101644
Ending digit 7: 2687 1907 47 227 2207 14867 3407, Total=89756
Ending digit 9: 1709 4289 509 929 269 449 24029, Total=78782

Solutions for R=8.

Ending digit 1: 26641 8941 3361 541 6481 12781 41761 51421, Total=489546
Ending digit 3: 22123 1723 1123 163 283 11083 42643 22963, Total=334188
Ending digit 7: 6277 8737 9397 13537 7717 17377 10837 26017, Total=428652
Ending digit 9: 499 15619 3019 5659 2179 23059 3739 19819, Total=312354

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Jan wrote:

Q3:

Solutions with R=8, bottom rows (not necessarily the least assignation):
Ending digit 1: 14051 22751  4691 10271 17891  6911 11411 12671
Ending digit 3: 34673 36473 35393 19913 19793 35993 14753  4073
Ending digit 7: 11617 14197  4177  6277 12097  6037  4657 13477
Ending digit 9: 13789 25609  1069  7129  3229  8329  4909 10009

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