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An Arrangement of 15 you were asked to place the numbers 1 to 15 in a line so that any two adjacent numbers summed to a square number.
Now, try to arrange the numbers from 1 to 32 in a circle, so any two adjacent numbers again sum a square number.
22, 27, 9, 16, 20, 29, 7, 18, 31, 5, 11, 25, 24, 12, 13, 3, 6, 30, 19, 17, 32, 4, 21, 28, 8, 1, 15, 10, 26, 23, 2, 14.
I started, like Larry, with subsequences, they can be joined to form the above solution, from 22 till 5, the rest is done by just trying all solutions.

Posted by Hugo
on 20050109 20:07:28 