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There is a relation between rectilinear-adjacent squares such that there is a unique rectilinear path from the top-left corner of the grid down to the bottom-right corner of the grid. Each square can participate in the path no more than once. What is the relation and the path it induces?

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Previous

Hint 1

The relation is inspired by a Project Euler puzzle.

Hint 2

The relation pertains to whether adjacent numbers are part of the same triplet.

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  • $\begingroup$ Care posting another hint? $\endgroup$ – Xnero May 14 '20 at 2:11
  • $\begingroup$ @Daniil Sure, I'll add another soon! $\endgroup$ – Galen May 14 '20 at 2:15
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The path is as follows

Solution Image

And the relationship is

Adjacent numbers are two members of a Pythagorean triplet

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Sorry, I did not see that someone posted an answer already.

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The relationship

The sum or difference of squares of the connected numbers is a square.

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