🔀 How to solve the 15 Puzzle step by step

By Miguel Arechaga

The 15 Puzzle is that square with numbered tiles and a gap that seems impossible to sort out once you shuffle it at random. The good news is there's a reliable method: follow it, and you'll always solve it. Here's the complete technique.

What is the 15 Puzzle?

It's a 4x4 sliding puzzle with 15 numbered tiles and one empty space. The goal is to arrange the tiles from 1 to 15 by sliding them into the gap. Our version always generates shuffles that have a solution.

How to play

1. Click a tile adjacent to the gap to slide it into place.
2. Keep going until all the tiles from 1 to 15 are in order, leaving the gap in the bottom-right corner.
3. The game counts your moves and your time: the challenge is doing it with the fewest possible.

The method that never fails

The strategy is to solve the puzzle in stages, without ever touching what's already placed:

1. Top row (1, 2, 3, 4): place the 1 and 2 first. For the 3 and 4, position them vertically in the right-hand corner and "rotate" them into place with a classic move. Once the top row is done, never move it again.
2. Left column (5, 9, 13): repeat the same idea with the first column. Now you have the top row and left column both fixed.
3. Remaining square: you're left with a 3x3 puzzle and then a 2x2 one, much more manageable. Solve it patiently by moving tiles in small circles.

Tips to improve your score

• Think two or three moves ahead before touching a tile.
• Never break apart a row or column you've already finished to place another piece.
• Once the puzzle is down to a 2x2, sometimes rotating the three remaining tiles in a circle is all it takes.

With this method you'll go from moving tiles blindly to solving it every time, and from there you can focus on lowering your move count.

🏆 Best-games ranking

The 15 Puzzle has its own global ranking: it saves your solve with the fewest moves. Go to Ranking, the 🕹️ 1 Player tab, choose "the 15 Puzzle" from the dropdown, and compare your score with other players, synced to your account. For your result to count you need a free account on MundoSudoku (just a username and password, no email required): you can play without one, but without signing in your score isn't saved to the ranking.