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The hole can occur at the center of a face or at a corner of the 3x3x3 cube.
Color the cubes in the 3x3x3 cube in a 3D checkerboard pattern. The eight cubes in the corners and the six cubes in the center of the faces will be one color, say black. The twelve cubes in the middle of each edge and the cube in the very center will be the other color, say white. There are 14 black cubes and 13 white cubes.
Each 1x1x2 domino will take up one white and one black cube, which means that the hole will be in the position of a black cube, which is at the center of a face or at a vertex of the 3x3x3 cube. |
