New Scientist #2623, Enigma #1462
From Albert Haddad, “Coloured Cubes”
In the following statements different capital letters in bold stand for different digits, with the same letter 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?
I don’t often attempt these puzzles (not the least because we only recently resubscribed), but this one I thought I could do. (Too frequently I find the puzzles to be too enigmatic.) And I was right! Including time wasted for a transcription error, it took me about 45 minutes to do this one. It took a small amount of puzzling in the beginning (no harder than Sudoku), and then I just did the second half brute-force, which is easy enough to do when there are only a few options to test.
I will admit to using a spreadsheet to do the calculations for me, but I didn’t use anything more sophisticated than multiplication with it.
Answer below the fold. I was disappointed to learn that the number didn’t spell anything.
There are 21,413 blue cubes in the remaining pile.
