Enigma 1462: Coloured cubes
12 February 2013
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From New Scientist #2623, 29th September 2007
In the following statements different capital letters in bold stand for different digits, with the same letter consistently standing for the same digit.
I have a collection of cubes in three different colours: red, blue and yellow. Their sides are all whole numbers, and furthermore I can tell you that the volume of each red cube is NIL, the face of each blue cube has NO area and the volume of each yellow cube is ZERO. Obviously the total volume of all the cubes is NOTHING. As for quantities, if you arrange the cubes into three distinct piles according to colour, you will find that in one pile there are NO cubes and in another pile there are NONE.
How many cubes are in the remaining pile, and what is their colour?