Solving the 15-Puzzle: Algorithms & Tricks
Solvability
Did you know that if you physically lift tiles out of a 15-puzzle and place them randomly, there is a 50% chance the puzzle is completely unsolvable? This is due to the parity of permutations. Our game uses a valid shuffle algorithm that works backwards from the solved state to ensure every puzzle can be won.
A* Search Algorithm
Computers solve sliding puzzles using graph search algorithms like A* (A-Star). They calculate the "Manhattan Distance" (total distance of all tiles from their home) and prioritize moves that reduce this number. Humans do this intuitively!
Strategy for Humans
You don't need to be a supercomputer. Start row by row.
- Solve the top row (1, 2, 3) first. Lock them in place.
- Solve the first left column of the remaining grid.
- Now you have reduced the 4x4 problem to a 3x3 problem. Repeat until you are left with just a 2x2 square to rotate.