I'm writing my BSc thesis on my favourite puzzle game from when I was a kid, called Lunar Lockout/Landing https://www.thinkfun.com/products/lunar-landing/. I'm trying to find the most difficult possible puzzles for varying sets of parameters. (As a metric for difficulty I've picked minimal number of moves to optimally solve.)
My question is: Does anyone know if this has been done before? And if not, I'm looking for related work for references. I know about god's number for the Rubik's Cube, but that's about it. Anything related, about single-player puzzle board game or similar, would be very much appreciated!
For anyone interested, I can already tell you god's number for the game is 14, given the constraints of the physical puzzle (5x5 square board with one "goal piece" and max 5 "non-goal pieces", with the goal in the middle of the board). There are 64 such puzzles (not filtered for symmetries yet). This is one of them (1 represents the "goal piece", 2 represents a "non-goal piece"):
0 0 2 0 1 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 2
Thanks in advance!