Number Slide

The 15-puzzle was invented in 1880 and immediately became a fad — newspapers offered cash prizes for solutions, math journals published proofs of solvability, and Sam Loyd claimed credit for inventing it (he didn't).

The math fact that changes everything

Of all 16!/2 ≈ 10 trillion possible scrambles, exactly half are unsolvable. A random shuffle has a 50/50 chance of being impossible. This game uses move-based shuffling instead, which guarantees solvability.

Optimal solution

The minimum number of moves for any solvable position is at most 80. Average random scrambles take 50-60 moves to solve optimally. Most casual players solve in 100-200 moves.