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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.
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The square tiling has 9 uniform colorings: 1111, 1112(a), 1112(b), 1122, 1123(a), 1123(b), 1212, 1213, 1234. In geometry, a uniform coloring is a property of a uniform figure (uniform tiling or uniform polyhedron) that is colored to be vertex-transitive.
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Example game of Dots and Boxes on a 2×2 square board. The second player ("B") plays a rotated mirror image of the first player's moves, hoping to divide the board into two pieces and tie the game. But the first player ("A") makes a sacrifice at move 7 and B accepts the sacrifice, getting one box.
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of {4,4}, meaning it has 4 squares around every vertex. Conway called it a quadrille. The internal angle of the square is 90 degrees so four squares at a point make a full 360
In the same way, the doubly triangular numbers also count the number of distinct ways of coloring the four corners or the four edges of a square with colors, allowing some colors to be unused and counting two colorings as being the same when they differ from each other only by rotation or reflection of the square. The number of choices of ...
The graph coloring game is a mathematical game related to graph theory. Coloring game problems arose as game-theoretic versions of well-known graph coloring problems. In a coloring game, two players use a given set of colors to construct a coloring of a graph, following specific rules depending on the game we consider.
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