13
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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 only once. What is the relation and the path it induces?

enter image description here

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  • $\begingroup$ lower right number is hard to spot: it is 25. $\endgroup$
    – daw
    May 11 '20 at 13:23
  • $\begingroup$ @daw Thanks for the clarification. I'll pick another colour in the future. $\endgroup$
    – Galen
    May 11 '20 at 13:35
  • $\begingroup$ Gur erdhverzrag gung nqwnprag ahzoref or pbcevzr erfgevpgf gur tevq dhvgr avpryl, ohg vg nccrnef gb or n erq ureevat abarguryrff. $\endgroup$ May 11 '20 at 14:12
  • $\begingroup$ @AxiomaticSystem Lrf, naq V znqr n eryngrq chmmyr gung qverpgyl hfrf aba-pbcevznyvgl. $\endgroup$
    – Galen
    May 11 '20 at 14:16
  • $\begingroup$ Any more hints? $\endgroup$ May 16 '20 at 5:42
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I believe

Every pair of numbers have no common factors (other than 1). So they are co-prime. Hopefully I haven't made a mistake... enter image description here

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  • $\begingroup$ rot13 (Fdhnerf ner abg cneg bs gur eryngvba, ohg gung vf na vagrerfgvat nccebnpu. Pbby.) $\endgroup$
    – Galen
    May 11 '20 at 14:12
  • $\begingroup$ Base64(VG9wIGxlZnQ6IDc1ICYgODggYXJlIGNvcHJpbWUgLCBhbmQgODggJiA0NSBhcmUgY29wcmltZSBhcyB3ZWxsLCBzbyB0aGUgcGF0aCBpc24ndCB1bmlxdWUgaWYgdGhlIHJlbGF0aW9uIGlzIGNvcHJpbWFsaXR5Lg==) $\endgroup$
    – naldjuno
    May 11 '20 at 15:41
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    $\begingroup$ Path is not unique with this relation. $\endgroup$ May 11 '20 at 21:16

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