A Tour Around a Triangle

Bernardo Recamán Santos 05/15/2018. 1 answers, 686 views
number-theory graph-theory arithmetic

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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1 Answers


F1Krazy 05/15/2018.

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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