A Memory-Efficient Method for Fast Computation of Short 15-Puzzle Solutions

While the 15-puzzle has a long and interesting history dating back to the 1870s, it still continues to appear as apps on mobile devices and as minigames inside larger video games. We demonstrate a method for solving the 15-puzzle using only 4.7 MB of tables that on a million random instances was able to find solutions of 65.21 moves on average and 95 moves in the worst case in under a tenth of a millisecond per solution on current desktop computing hardware. These numbers compare favorably to the worst case upper bound of 80 moves and to the greedy algorithm published in 1995, which required 118 moves on average and 195 moves in the worst case.