[possible spoilers] Well-known data-structure the key?

[Allosentient]

Has anyone ever applied the 1873 (yes, 19th century) Hierholzer's algorithm to this problem? I have a hunch that building a graph and using this algorithm would do the trick, but haven't had the time to prove it.

At the time I was doing these problems in 2008, graphs (as a data structure) were not a concept known to me. I was a 21-year-old college dropout, with only two compsci classes ever completed.

I'm curious if anyone's ever experimented with using Hierholzer's on this problem.

[Hippo]

I don't think the mentioned algorithm helps here.