Enigma 1735: A pile of coloured cubes
6 February 2013
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From New Scientist #2903, 9th February 2013 [link]
I have several boxes, each containing a number of cubes. Each cube has black and white faces (at least one of each colour per cube), and each box contains all possible different cubes, with no duplicates. My three nephews opened the first box and each tried to assemble their own 2×2×2 cube with only one colour on its outer faces, and of course they failed. They then opened further boxes until they were each able to assemble a single-coloured 2×2×2 cube. They then put all the leftover cubes from the open boxes in a pile.
How many cubes were there in the leftover pile?