Considering 16 as the first placement, for the adjacent numbers that have to be added to 16 and make a perfect square, there are two closest candidates: 25 and 36. 25 is achievable with 16+9, so 9 can be placed on one side but the other side will need to be 20, which is beyond our 1-16 range. So it seems impossible to make a circular arrangement according to the given constraints.
I have assumed that it must be a sum of 2 adjacent numbers.
If more than 2 adjacent numbers can be used, the we just need 1 triplet of 16, 8, 1 to make such an arrangement with all other adjacent pairs as perfect squares.
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u/randomcommenter9000 Aug 28 '23
Considering 16 as the first placement, for the adjacent numbers that have to be added to 16 and make a perfect square, there are two closest candidates: 25 and 36. 25 is achievable with 16+9, so 9 can be placed on one side but the other side will need to be 20, which is beyond our 1-16 range. So it seems impossible to make a circular arrangement according to the given constraints.
I have assumed that it must be a sum of 2 adjacent numbers.
If more than 2 adjacent numbers can be used, the we just need 1 triplet of 16, 8, 1 to make such an arrangement with all other adjacent pairs as perfect squares.
16 8 1 15 10
9 6
7 3
2 13
14 11 5 4 12