While poking around some old files I came across this puzzle:
(Click for a larger version.) I didn’t make it, and I have no idea where I got it from (do you know?). But in any case, wherever it comes from, I think it’s a really great puzzle. I did find the number that can make it through the diagram, but I never did completely finish proving that the solution is unique.
Can you solve it? Let’s see if we can prove it together. Please don’t post the number in the comments. But please do post proofs that certain combinations of nodes are impossible. For example, you might post a proof that no triangular number can be one more than a prime; that would mean the leftmost path is impossible.