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

***

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

***

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

***