[danvk]

> “As far as I can tell, I’m the only person who is actually interested in this problem,” Vanderkam said.

For context, many people are interested in finding high-scoring Boggle boards, usually via simulated annealing, hillclimbing, or genetic algorithms. But so far as I can tell, I'm the only one interested in _proving_ that a particular board is best. Doing that was the new result here.

[hamburglar]

I once spent a little time writing code to find the longest possible boggle word and found there were a few candidates. Interesting things I noted that weren’t entirely obvious: the longest word is actually 17 characters, not 16, because of the “Qu” side, and there are actually lots of words that are impossible, because for example there is only one J and only one B and they are on the same die.

I don’t remember all the longest words but sesquicentennials was one of them.

[danvk]

Finding the highest-scoring board with a 16- or 17-letter word is a fun, but very different problem. There are few enough "Hamiltonian paths" through the all the letters on a 4x4 Boggle board (~68,000) and few enough 16 letter words (~2,000) that you can enumerate all pairs in an hour or two.

Depending on wordlist and whether you want a 16 or 17 letter word, you get "charitablenesses", "supernaturalised" (British spelling), "quadricentennials" or "quartermistresses". These boards all score considerably lower than the REPLASTERING board. Full results here: https://github.com/danvk/hybrid-boggle/#highest-scoring-boar...

I hadn't realized until I did this "side quest" that most wordlists top out at 15 letter words. That makes sense for a Scrabble dictionary, but it's not great for Boggle.