How to solve the 15 puzzle

The 15 puzzle looks impossible at first, but a simple layer-by-layer method solves every board. No luck needed.

The idea: shrink the puzzle

Don’t try to place all tiles at once. Solve the top row, then the left column. What remains is a 3×3 puzzle (the 8 puzzle), which you solve the same way. Never move a finished tile again; route other tiles through the unsolved area.

Step 1: the top row (1, 2, 3, 4)

1. Move tile 1 to the top-left corner, then tile 2 next to it.
2. Tiles 3 and 4 need a trick, because placing 3 first blocks the corner for 4. Instead, put 4 in the spot where 3 belongs and 3 just below it.
3. Now move the gap to the top-right corner and slide 4 right, then 3 up. Both drop into place together.

Step 2: the left column (5, 9, 13)

Use the same trick vertically: place 5, then put 13 where 9 belongs and 9 just to its right, and rotate them in together.

Step 3: finish the 3×3

You now have a 3×3 area with tiles 6, 7, 8, 10, 11, 12, 14, 15. Solve its top row (6, 7, 8) with the same corner trick, then its left column (10, 14), and finally cycle the last 2×2 (11, 12, 15 and the gap) until it lines up.

Tips

• If the last three tiles never line up however you cycle them, re-check the rows you finished earlier: one tile there is out of place. Every shuffle on this site is solvable.
• Learn on the 3×3 board first, then move to 4×4 and 5×5.
• A good 4×4 solve takes under 100 moves; your best is saved automatically.