15 Puzzle

The 15 Puzzle dates back to the 1870s and is linked to Noyes Palmer Chapman, even though Sam Loyd later made the unsolvable 14-15 swap famous with a prize challenge. The puzzle uses fifteen numbered tiles and one empty space on a 4x4 board. Your goal is to restore order by sliding tiles into the blank. The mathematical hook is parity: not every scrambled board can be solved. Start with a valid shuffle, solve row by row, and finish with the final cycle.

1. Slide a tile into the empty space.
2. Arrange the first row in order: 1, 2, 3, 4.
3. Solve the second row while preserving the first.
4. Build the lower rows and columns carefully.
5. Use the blank space to rotate small groups of tiles.
6. Win when tiles read 1 through 15 with the blank at the end.

• Only tiles next to the blank can move.
• A move slides one tile into the blank square.
• Tiles cannot jump over each other.
• The standard puzzle uses a 4x4 grid with numbers 1 through 15.
• Only parity-valid shuffles are solvable.
• The solved state places the blank in the lower-right corner.

• Solve the top row first, then avoid disturbing it.
• Place the last two tiles of a row as a pair. For example, set 3 and 4 together before locking row one.
• Use 2x3 rotation areas to reposition tiles without breaking solved rows.
• Save the final two rows for a cycling method rather than solving one tile at a time.
• If 14 and 15 are swapped at the end, the starting position was unsolvable or a solved row was disturbed.

• Sliding Puzzle: The broader sliding-tile format with multiple grid sizes.
• Sokoban: A movement puzzle with box pushing and deadlock planning.
• 8 Puzzle: A smaller 3x3 version using eight tiles and one blank.

• The physical movement is easy to understand.
• Parity gives the puzzle a real mathematical backbone.
• Solving rows creates steady progress.
• The final cycle is tense even after a good solve.

Play the 15 Puzzle online for free. Slide tiles, restore the numbered order, and learn the row-pair method that makes the puzzle much easier to control.

The 15 Puzzle is a sliding-tile test of order, parity, and controlled movement. Solve rows in pairs, protect finished sections, and use the blank as your steering tool.

• 15 Puzzle History and Parity
• 15 Puzzle Parity Rule