olligobber

Never mind. Typing that number into a search revealed a paper from 2012 that found it first. https://www.researchgate.net/publication/290264363_On_the_Difficulty_of_Nonograms

Hmm, the 2020 paper linked on that page does give a number for how many 6x6 nonograms are locally solvable, but that number is somehow less than the number it gives for 5x6 nonograms that are locally solvable? This seems impossible to me, since every locally solvable 5x6 nonogram has a corresponding locally solvable 6x6 locally solvable nonogram where the last row is empty. I guess I'll have to work on my code to find out how many locally solvable 6x6 nonograms there actually are... and maybe even 7x7?

@voxel@merveilles.town https://oeis.org/A053169

It would help if I read the paper properly. They only looked at a random sample of about 1% of the puzzles, so the actual number would be about 100x bigger than theirs, which makes sense. Still, they say it's computationally infeasible to find the actual number, but my estimates say it would take 10 days running on a single processor of my laptop.

@slava Huh, from that definition it's not even clear to me that the monoid is finite. Don't spoil the proof for me though!

@ericwastl@hachyderm.io Thank you so much for all the hard work you put in.