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?
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.)