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.
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: