I have read that the hardest 8 puzzle requires 31 steps to solve, i.e. every solvable 8 puzzle can be solved in max. 31 steps. How is that?
2026-02-23 10:20:31.1771842031
Maximum of minimum number of moves required for hardest 8 puzzle
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The wikipedia link for the 15 puzzle points to an OEIS link which points to a paper "Complete Solution of the Eight-Puzzle .." by Alexander Reinefeld. (The link in the OIES page is bad.) The distribution of solution lengths and the maximum length 31 were obtained by exhaustively evaluating all $9!/2$ configurations.