MacMahon Squares is the name given to a recreational edge-matching puzzle first published by Captain Percy MacMahon in 1921, where 24 uniquely 3-colored squares are organized next to each other by matching color to create a 4 by 6 grid. Such puzzles have multiple variants, which are determined by restrictions on how to arrange the 24 squares. This game has also been commercialized in numerous physical forms, by various companies. History MacMahon squares was first published in Percy Alexander MacMahon's 1921 treatise New Mathematical Pastimes , consisting of the unique set of 24  squares that can be made by coloring the edges  with one of three colors.  As MacMahon Squares are isomorphically equivalent to edge-matching puzzles, they are NP-Complete Rules Each of the 24 squares, arranged in a 4 by 6 grid, are composed of 4 triangles. Each of the 4 triangles is assigned a color, to create 24 distinct squares. Alternatively, it can also be viewed as 24 squares consisting of each of the 24 possible permutations of 3 colors for the 4 edges. Squares can be rotated, but not flipped. There are a total of 24 distinct squares for 3 colors. For a given number of colors, the number of squares can be found by the expression  Contact System MacMahon suggested, in his book,  the ability to define which borders can contact one another, based on their colors. This is by some permutation of the 3 colors, described by Ca,b,c. Here, a, b, and c represent the shift in colors to which the first, second, and third colors can be matched to. A '1' it is matched to itself, and a '2' signifies that it must be matched with a different color. Analogous Puzzles MacMahon Squares, along with variations on the idea, was commercialized as Multimatch.
MacMahon Squares is the name given to a recreational edge-matching puzzle first published by Percy MacMahon in 1921, where 24 uniquely 3-colored squares are organized next to each other by matching color to create a 4 by 6 grid. Such puzzles have multiple variants, which are determined by restrictions on how to arrange the 24 squares. This game has also been commercialized in numerous physical forms, by various companies. The game MacMahon squares was first published in Percy Alexander MacMahon's 1921 treatise New Mathematical Pastimes . The original version consisted of one copy of each of the 24 different squares that can be made by coloring the edges of a square with one of three colors. (Here "different" means up to rotations.) The goal is to arrange the squares into a 4 by 6 grid so that when two squares share an edge, the common edge is the same color in both squares. The MacMahon Squares game is an example of an edge-matching puzzle. The family of such problems is NP-Complete. There are a total of 24 distinct squares for 3 colors. For a given number of colors, the number of squares can be found by the expression . Contact system In his book, MacMahon suggested the ability to define which borders can contact one another, based on their colors. This is by some permutation of the 3 colors, described by Ca,b,c. Here, a, b, and c represent the shift in colors to which the first, second, and third colors can be matched to. A '1' it is matched to itself, and a '2' signifies that it must be matched with a different color. Analogous puzzles MacMahon Squares, along with variations on the idea, was commercialized as Multimatch.
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