Christopher Janjigian

Outreach module (grades 9-12)

Fifteen Puzzle Explorer

Part 1: Play the puzzle

Module Sequence

1. Play the puzzle 2. Parity 3. Permutations 4. Length and parity 5. Solvability 6. Solution guide

Goal

Rearrange the tiles into increasing order, reading left to right and top to bottom, with the empty space in the bottom-right corner.

As this module will show, some starting boards can be solved and some cannot. The goal is to understand when and why the game is solvable, and then to learn how to solve solvable boards systematically.

Goal board layouts. The 15 puzzle goal has rows 1, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11, 12; and 13, 14, 15, blank. The 7 puzzle goal has rows 1, 2, 3, 4 and 5, 6, 7, blank.

15 puzzle goal
7 puzzle goal

Play

Focus the board, then use Arrow keys or WASD. Click or tap a neighboring tile to slide it.

15 puzzle board. 4 rows and 4 columns. Blank at row 4, column 4.

Puzzle selector

Choose a start and make your first move.

Stats

Moves: 0

Time: 00:00

Best solved runs: none yet

Board state

2: Parity

Loyd's problem and the power of parity.