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Segerman's 15+4 puzzle is a hinged version of the classic 15-puzzle, in whichthe tiles rotate as they slide around. In 1974, Wilson classified the groups ofsolutions to sliding block puzzles. We generalize Wilson's result to puzzleslike the 15+4 puzzle, where the tiles can rotate, and the sets of solutions aresubgroups of the generalized symmetric groups. Aside from two exceptionalcases, we see that the group of solutions to such a puzzle is always either theentire generalized symmetric group or one of two special subgroups of indextwo.

Sliding Block Puzzles with a Twist: On Segerman's 15+4 Puzzle