How to solve Sliding Tiles: the 15 puzzle method

Every sliding tile puzzle can be solved with one simple method. It isn’t the fastest, but it always works, and once you know it you can start chasing your best time.

The rules

The board holds numbered tiles and one empty space. Slide a tile into the space, one at a time, until the tiles read in order from 1 at the top left, across each row, with the space in the bottom right. On BoardGameSite you can tap any tile in line with the space to slide several at once.

Step 1: solve the top row

Bring the 1 into the top-left corner, then the 2 beside it, and so on. Moving a tile into place is a matter of walking the space around it: put the space next to the tile on the side you want it to move toward, then slide it in.

Step 2: the last two tiles of a row

The last two tiles of a row are the tricky part, because placing one knocks the other out. The fix is to place them together:

1. Put the last tile of the row (for example 4) into the corner where the one before it (3) belongs.
2. Put the one before (3) directly underneath it.
3. Bring the space into the last spot of the row, then slide 4 across and 3 up. Both drop into place.

Step 3: repeat, row by row

Once the top row is done, never touch it again. Solve the next row the same way. Keep going until only two rows are left.

Step 4: the last two rows, column by column

With two rows left, switch direction. Solve the left column of those two rows: the top tile and the tile below it, using the same pairing trick turned on its side. Then the next column, and so on, until the last few tiles rotate into place.

Getting faster

Once the method feels natural, look for shortcuts: moving the space the short way round, and setting up the next tile while you place the current one. The best players solve the 4×4 puzzle in well under a minute.

A bit of history

The 15 puzzle swept the world in 1880. Newspapers offered prizes for an impossible version where the 14 and 15 were swapped. No such puzzle can be solved, which is why every puzzle here is made by shuffling a solved board with real moves.