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Dicey numbers

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?

£15 will be awarded to the sender of the first correct answer opened on Wednesday 14 January. The Editor’s decision is final. Please send entries to Enigma 1523, New ÐÓ°ÉÔ­´´, Lacon House, 84 Theobald’s Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address). The winner of Enigma 1517 is J. Lunn of Chelmsford, Essex, UK.

Answer to 1517 Just forgotten

Joe’s 10-digit account number was 9624317850