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Place the 18 even integers between 2 and 36 in the empty nodes of this triangular graph in such a way that if a path is drawn by coloring in red all the edges joining any two nodes whose numbers add up to a square, that path, beginning at 1, will visit every node precisely once, and finally connect back with 1.

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There are a few nodes that can be linked together immediately, giving us a good starting point:

Most of those starting links are on the bottom half of the triangle, so that's where I started. Specifically, I was quickly able to fill in the bottom-right:

Followed by the rest of the bottom:

The next bit threw me briefly, but I managed to figure out the placement of the numbers and joined back up with the start point:

And from there, with only a few numbers remaining, it was easy to fill in the rest, leaving us with the final path:

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    $\begingroup$ LOL at the fact you're doing this at work! $\endgroup$
    – Phylyp
    May 15, 2018 at 17:00
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    $\begingroup$ My shift was nearly over, and I'd spent most of the day bashing my head against three separate brick walls. This was actually quite relaxing. $\endgroup$
    – F1Krazy
    May 15, 2018 at 18:38
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    $\begingroup$ Doing puzzles at work and bashing your head against walls? Let me guess, you are a programmer. $\endgroup$
    – Gustavo Gabriel
    May 15, 2018 at 18:51
  • $\begingroup$ @GustavoGabriel Yep. You'd be surprised how many of my answers were written while I was at work... or maybe you wouldn't, idk. $\endgroup$
    – F1Krazy
    May 15, 2018 at 19:11

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