🔣Play Tile Slide

The sliding tile puzzle is one of the oldest mechanical puzzles still in circulation, and it caused a genuine craze in the 1880s when a version was sold with two tiles deliberately swapped and a cash prize attached. The prize was safe: that arrangement is mathematically impossible to solve, and proving why is a small classic of permutation theory.

Exactly half of all possible tile arrangements can be solved. Whether a board is solvable depends on the parity of the permutation combined with the row the gap sits in, and no sequence of legal moves can ever change it. This is why our board is scrambled by making hundreds of random legal moves from the solved state rather than by shuffling the tiles — a shuffled board would be unwinnable half the time.

The solving technique is layered rather than clever. You place the top row, lock it, place the next row, lock it, and finish with the bottom two rows, which have to be solved together because there is no longer room to manoeuvre. The last three tiles are where most people get stuck, and the answer is almost always to cycle the 2x2 rather than to panic.

Your move count is the score and lower is better. A confident solve lands somewhere between eighty and a hundred and fifty moves; the theoretical worst case for a 4x4 board is eighty moves, but only with perfect play that no human produces at speed.