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The Mayblox Problem

One of the treasures of a “turn-of-the-century” child was a small box bearing the inscription Mayblox. 1 The box contained eight wooden cubes, each of which displayed the six colors, red, yellow, white, purple, green, and black — one color to a face. The player was instructed to form one large cube from the eight small ones such that each face of the large cube would be solidly colored and so that contact faces of the small cubes would be of the same color. The child might stumble for hours before solving the puzzle, but the Mayblox poses further questions of a more general nature than the construction of one suitable cube.