Solving sliding tiles row by row

Sliding puzzles look chaotic, but one method solves any size reliably. You build the picture from the top, lock away finished rows and make the board smaller step by step.

The first row

Bring the tiles of the top row into place one by one, left to right. To move a tile, bring the gap next to it on the side you want it to go, then slide it. Moving a tile one step usually means walking the gap around it in a small loop.

The corner trick

The last two tiles of a row cannot simply be pushed in one after the other. Put the second-to-last tile in the last position of the row, put the last tile directly beneath it, then bring the gap to the empty position in the row and slide both tiles over: the first moves left, the second moves up. The row is complete without breaking anything.

Down to two rows

Repeat row by row until only two rows remain. Then switch to columns: solve the last two rows column by column from the left, pairing the top and bottom tile of each column with the same trick turned on its side.

The final square

The last 2×2 square contains three tiles and the gap. Rotate the three around the gap until they line up; because the deal is solvable, they always do.

When the picture is plain

Turn on the numbers for rows of sky, snow or fog. Numbers run left to right, top to bottom, the same order the method follows. Once the detailed part of the picture appears, switch them off and finish by eye.