Three Ways to Solve Domino Grids
Ken Caviness · The Mathematica Journal · 2014
This article develops and compares three methods for solving domino grid puzzles: a "human-type" algorithm, a brute-force method, and a scheme using a generalized odometer. ‡ A Puzzle Is Presented, and a "Human-Type" Solution Algorithm DevelopedWhen my son brought home a paper from school with a 7 µ 8 grid of numbers on it, I was immediately interested.The goal: cover the puzzle with all the dominoes from the "bone pile," making sure that each number of the puzzle is covered by the same number on a domino.Many similar puzzles can be found online and in puzzle collections: see [1, 2, 3, 4, 5] for several online resources, which are the source of some of the examples considered here.4 4 0 0 1 2 6 6 2 2 4 1 2 0 0 6 6 6 5 2 0 2 2 2 1 3 3 5 5 5Ú Figure 1.A partially solved domino grid, with almost half of the 28 dominoes placed on the underlying puzzle grid.