SFU Math

Permutation
Puzzles

A collection of puzzles exploring permutation groups, cycle structure, transpositions, and the hidden group theory behind sliding tiles, oval tracks, and combinatorial brainteasers.

Swaps

Swap Puzzles

Swap

Rearrange tokens by sliding and swapping adjacent pairs — explore which permutations are reachable.

Play →

Swap: 2-Cycles

Every permutation is a product of transpositions — discover parity through 2-cycle decomposition.

Play →

Swap: 3-Cycles

Restrict swaps to 3-cycles — which permutations remain reachable? Parity takes on a new meaning.

Play →

Flips

Flip Puzzles

Flip

Flip an adjacent pair of two tokens to reverse their order — reach the target arrangement.

Play →

Flip Any Two

Choose any two tokens and swap/flip them simultaneously — a different generator set, a different group.

Play →

Sliding Tiles

Sliding Tile Puzzles

15-Puzzle

Slide 15 numbered tiles into order — exactly half of all scrambled positions are solvable.

Play →

15-14 Problem

The classic unsolvable position — tiles 14 and 15 swapped. Understand why parity forbids it.

Explore →

15-Puzzle: Blockage

A wall blocks certain moves — how does a single barrier reshape the reachable permutations?

Play →

Rate Your Mind Pal

A vintage thinking puzzle — slide pieces around to restore the phrase.

Play →

Panama Canal

The P and C have been swapped — can you restore them to their proper place?

Play →

Get My Goat

Slide tiles around the board to capture the goat inside the fence — parity lurks in every move.

Play →

Classics

Classic Permutation Puzzles

Oval Track

Rotate tokens around an oval and apply a turntable move — a group generated by two permutations.

Play →

Oval Track: Flip

The oval track with a flip move added — explore how an extra generator expands the group.

Play →

Pop Culture

Pop Culture Puzzles

Futurama Theorem

Bodies are swapped but the machine can't reuse a pair — prove you can always undo the mess.

Play →