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Tile Slide is the sliding-tile puzzle — fifteen numbered tiles and one gap, to be arranged in order. It has been around since the 1870s, and it has a genuinely interesting mathematical property: exactly half of all possible starting arrangements cannot be solved at all.
Tiles are scrambled with one empty space.
Click a tile adjacent to the gap to slide it in.
Work tiles into their correct positions.
Arrange them all in order to solve the puzzle.
Larger grids unlock as you succeed.
Sequential planning and the discipline of not undoing your own work. The characteristic difficulty is that finishing the puzzle requires temporarily disturbing tiles you have already placed.
Solve the top row completely, then the left column, then repeat on the smaller remaining square.
For the last two tiles of a row, place them together using the standard three-move cycle rather than one at a time.
Never break a completed row or column except through that cycle.
Work towards the bottom right. The final 2×2 corner is solved last and by rotation.
Not in general — exactly half of all arrangements are unreachable, a result proved in the 1870s. Our scrambles are produced by making legal moves from a solved state, so every puzzle you receive is solvable.
Solve the top row and left column, then treat the rest as a smaller puzzle and repeat. The final 2×2 corner is solved by rotation.
Because rows must be finished two tiles at a time. Placing the last one individually strands it, which is the classic beginner trap.
Every position has one, and finding it is a hard computational problem. Efficient human play is about method, not optimality.