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The puzzle is impossible to complete. A domino placed on the chessboard will always cover one white square and one black square. Therefore, any collection of dominoes placed on the board will cover equal numbers of squares of each color. But any two opposite squares have the same color: both black or both white.
Following Grünbaum and Shephard (section 1.3), a tiling is said to be regular if the symmetry group of the tiling acts transitively on the flags of the tiling, where a flag is a triple consisting of a mutually incident vertex, edge and tile of the tiling. This means that, for every pair of flags, there is a symmetry operation mapping the first ...
Re-sawing is the splitting of 1-to-12-inch (25–305 mm) hardwood or softwood lumber into two or more thinner pieces of full-length boards. For example, splitting a 10-foot-long (3.0 m) 2×4 (1 + 1 ⁄ 2 by 3 + 1 ⁄ 2 in or 38 by 89 mm) into two 1×4s (3 ⁄ 4 by 3 + 1 ⁄ 2 in or 19 by 89 mm) of the same length is considered re-sawing.
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