Jigsaw Puzzles and The MacMahon Squares |

Written by Joe Celko |

Thursday, 08 February 2018 |

Another puzzle featuring Joe Celko's characterful pair, Melvin Frammis, an experienced developer at International Storm Door & Software, and his junior programmer sidekick, Bugsy Cottman. This classic puzzle looks deceptively simple but can you produce some beautiful code to solve it?
grumbled Larry Smead as he sat down at the break table at International Storm Door & Software.
“ “ Bugsy decided not to ask which ex-wife. Melvin Frammis walked over to the table with his drink and candy bar.
“
Larry's OCD kicked in and he wandered off talking to himself and drawing pictures on a paper napkin.
## ChallengeYour problem, dear reader, is to find all of the tilings with the all-white tile in the upper left corner. For example, you can start to put tiles the together like this: but not like this: : You can see that it is an interesting combinatorial problem to place all of the tiles together in a grid so that they obey the matching edges rule. It isn't even obvious that it can be done at all. This puzzle is a version of MacMahon squares, after their inventor, Percy Alexander MacMahon (1854-1929), an English mathematician and author of See the side panel for these and for other books that include it.. You'll find a good explanation of MacMahon 3-Color Squares on this blogspot and the entry in The Encyclopedia of Science also introduces 4-color triangles. If you want to go even futther see MacMahon's Coloured Cubes For bonus points, you can try to solve the Multimatch puzzle from from Kadon Enterprises http://www.gamepuzzles.com/edgemtch.htm#M1.
These square dominoes use all possible combinations of three colors on the edges of the dominoes, to give a set of 24 pieces. Kadon Enterprises deserves a shameless plug for their fine puzzles and games and I would recommend getting their catalog. ## Update:Reader Frans Faase wrote a program to find the solutions.
You can see all 46 solutions on his website which is well worth a visit for other topics. If you would like to send in a solutions to this puzzle email editor@i-programmer.info. Or use the comments below to discuss how to approach it.
## More puzzles tackled by Melvin, Bugsy & coVertex Coverings And The Cool Kids Problem Sharpen your Coding Skills - Elevator Puzzle ## Related articlesUnshuffling A Square Is NP-Complete
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Last Updated ( Sunday, 13 January 2019 ) |