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A pile of coloured cubes

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?

WIN £15 will be awarded to the sender of the first correct answer opened on Wednesday 6 March. The Editor’s decision is final. Please send entries to Enigma 1735, New Å®ÉúСÊÓƵ, Lacon House, 84 Theobald’s Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).

Answer to 1729 Xmas gifts: A, N, S, W, E and R are 17, 4, 3, 26, 5 and 9

The winner Christopher R. Jeggo of Woking, Surrey, UK