Enigma 1488: Cube turn
20 November 2012
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From New Scientist #2650, 5th April 2008
I have three cube-shaped dice and on each face of each die there is a non-zero digit. For each of the three dice the sum of its six different digits is the same odd total. (Incidentally, the digits are unambiguous: 6s cannot be read as 9s etc.)
I have been experimenting with these dice and, appropriately, with some numbers which are cubes. I find that it is possible to arrange the dice so that the three uppermost faces together read 125; then when I turn the three dice completely over, the new uppermost faces can be arranged to read 216. Similarly, the dice can be arranged to read 343 and then turned over and arranged to read 729.
Having had some success with cubes, I then looked at some squares. The dice can be arranged to read 169 and then turned over and arranged to read 256. And they can be arranged to read 361 and then turned over and arranged into another perfect square.