Six mathematically brutal puzzles

IMPOSSIBLE GAMES

These puzzles share one property: provably exponential or NP-hard complexity. Small inputs require astronomical moves. Pick one.

🗼

Tower of Hanoi

Recursive · Exponential

Move all rings from peg A to C, never placing a larger ring on a smaller. 64 rings = 584 billion years.

2ⁿ−1

→

🌀

Spin-Out

Chinese Rings · Exponential

Flip spinners to all face down. You can only flip the rightmost, or the one left of the rightmost "on" spinner.

2ⁿ⁺¹−1

→

💡

Lights Out

NP-Hard · Toggle Puzzle

Press a light to toggle it and all its neighbors. Some boards are provably unsolvable — can you tell which?

NP-hard

→

🥞

Pancake Sorting

Prefix Reversal · Unsolved

Insert a spatula anywhere and flip the top N pancakes. Sort them largest-to-bottom. Optimal count is unsolved for large N.

~(5/3)n

→

🪙

Turning Turtles

Nim Variant · Binary

Flip any heads coin to tails + optionally flip one coin to its left. Force your opponent to flip the last head. Nim logic governs everything.

Nim-value

→

🕐

Rubik's Clock

Gear Puzzle · 14 billion states

9 clock dials all connected. Turn any dial — others follow. Get all 9 to point to 12. 14 billion permutations.

~14B states

→