Sliding Puzzle

About this test

The sliding puzzle is a mechanical brain-teaser from the second half of the nineteenth century: a frame, fifteen numbered tiles, one empty space, and one legal move — sliding a tile adjacent to the gap. It caused a considerable international craze in the 1880s, fuelled by public challenges offering a reward for solving certain positions.

Those challenges were rigged, and the reason is mathematical: only half of all possible arrangements are reachable. The puzzle's elementary move can never simply swap two tiles, so one shuffle in two is strictly unsolvable. The board here is always generated from the solved position by a run of legal moves, so it always has a solution.

The method that works is hierarchical, and it's the opposite of intuition. You don't nudge tiles toward their slots one at a time: you complete the first row entirely, then declare it off limits, then the second, and you solve the last two rows together working in columns of two. Players who pass three hundred moves are nearly always the ones who break a finished row to gain one tile.

How it works

We count the slides needed to reach the full order 1 to 15 with the empty space bottom right. Giving up counts as a failure and scores zero. For a solved board, the 0-100 score starts at 400 moves and maxes out at 60.