Permutation along the circle

It is required to arrange a permutation of the numbers from 1 to 32 along the circle so that any two adjacent numbers in the sum give a perfect square.

What is the sum x + y + z x+y+z terms of this sequence (see picture)?

57 60 62 66 69 72

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1 solution

Michael Mendrin
Jun 12, 2018

1 , 15 , 10 , 26 , 23 , 2 , 14 , 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, 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

Tried out 31! different permutations to see which would work!

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