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Inspired by Galen's series of puzzles...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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  • $\begingroup$ Any comments on my answer? $\endgroup$
    – Culver Kwan
    May 19, 2020 at 5:30

2 Answers 2

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Path(Sorry, but I did on my IPad:

enter image description here

Relation:

Difference adjacent numbers is a power of 2

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  • $\begingroup$ Perfectly correct! $\endgroup$
    – Jeremy Dover
    May 19, 2020 at 5:32
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enter image description here
Absolute differences between successive terms are all squares.

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  • $\begingroup$ yes, this is a path but the relation does not satisfy all of the conditions of the question. $\endgroup$
    – Jeremy Dover
    May 19, 2020 at 1:06
  • $\begingroup$ This path is unique under the given relation; what condition is being violated? $\endgroup$
    – AxiomaticSystem
    May 19, 2020 at 2:41
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    $\begingroup$ I think you need to check that again. The path is not unique under the given relation. $\endgroup$
    – Jeremy Dover
    May 19, 2020 at 2:50
  • $\begingroup$ Agh, you're right. There's two paths, and rot13(obgu pbagnva ercrngf fb V'z abg fher juvpu bar vf gur pbeerpg bar, vs rvgure vf.) $\endgroup$
    – AxiomaticSystem
    May 19, 2020 at 3:06
  • $\begingroup$ Neither can be correct, since the relation does not produce a unique path. Don't feel bad though, I did my best to bait exactly this trap :-) $\endgroup$
    – Jeremy Dover
    May 19, 2020 at 5:26

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