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My friend Johan de Ruiter has made a nice puzzle for Donald Knuth's Birthday. The numbers indicate how many connections that candle has. Can you solve it?

Original link: https://www-cs-faculty.stanford.edu/~knuth/pi_hamilton_maze.png

enter image description here

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  • $\begingroup$ Are we to assume you can't visit a candle more than once, or just that you can't extinguish it more than once? $\endgroup$ – msh210 Mar 17 at 11:13
  • $\begingroup$ you can't visit it more than once. $\endgroup$ – Dmitry Kamenetsky Mar 17 at 11:20
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Solution:

enter image description here

It's actually quite straightforward to solve; at each step

you identify a vertex where there's no choice given the other information you already have. The only slight subtlety is that at one point I had to reason as follows: I already have 6-4-8 or 8-6-4, so 5 can't connect to both. (At that point there were 3 things the 5 could connect to.)

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