Enigma 1523: Dicey numbers
30 July 2012
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From New Scientist #2685, 6th December 2008 [link]
I threw a small number of standard dice and noted that the grand total of spots on the tops was a perfect square. Then I put the dice in a row in increasing order of their tops and wrote down the large number so formed (for example, 12224…).
Then I repeated the exercise with double the number of dice. Again the total number of spots was a perfect square, and again I wrote down the number formed by the tops in increasing order. It turned out that the second number I wrote down was the square of the first.
Incidentally (although you do not need to know this) throughout the exercise I threw at most one 6.
What was the second number that I wrote down?