I'm not sure that he does, I thought the same of the ad and didn't say anything but I was glad someone did.
Reading in the graph and putting it in a tree structure is a reasonable problem, but not a 10 minute interview one.
Traversing the graph to find the optimal path? Wow, that's known to be a tricky problem. Brute force search will work but will take a while. Now, undoubtedly there must be some very clever proof that discards most of the searches for the special case of a triangle structure. And if you've seen that you're all set. If not, hopefully you have your copy of AoCP at hand to start looking for it. If you are in an interview and haven't seen it, you just need to recreate the conditions from 1 million BC to 1950 or whenever someone had the right insight to come up with a proof. Not really a reasonable assumption. In those circumstances it's only a test of if you've run into this issue before.
And figuring out the answer is necessary to determine the email to submit a resume? How foolish that hiring manager is. If he was Google, yeah, you can put the question on a giant billboard ad as a challenge and get some responses. He's not Google.
Reasonable question is if someone can parse some data and put it in a tree or graph.
Reasonable interview question is to bring this up and talk about approaches. Person mention's Djikstra's algorithm, well he's heard of Djikstra and knew he was big on optimal path searches. Mentions AoCP, he knows a good place to look for clever algorithms. Knows how to solve it on the spot? Probably pretty clever. Finding the optimal 100 node long path in a graph as a screening method to send in a resume? Funny stuff there.
Being a bit clever myself though I'll go a bit further here. I'd say you might be the person who posted that ad. But I think more likely is you want to apply for the job and have no idea at all how to solve that problem and are hoping by coming here and pretending it is trivial someone like me will give you some hints. Because if you really knew your stuff, you wouldn't be claiming it was trivial for any competent practitioner to solve and a reasonable screening question.
Sure, there is an easy answer out there for doing this search, that's almost certain. That everyone competent would figure it out easily? Nah.