Three Ways to Solve Domino Grids

Abstract

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 Developed When 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. • Puzzle Construction ü Board Our first task is to represent the board. m9 = 8