GAME & ENTERTAINMENT – PUZZLE & CAUAL GAME CALCULATOR
Sliding Puzzle Moves
A precise tool.
What is the Sliding Puzzle Moves & How does it work?
A sliding (or 15‑) puzzle consists of N×N tiles numbered 1 … N²‑1 and one empty space. The objective is to reach a goal configuration by sliding tiles into the blank.
The most common admissible heuristic is the sum of Manhattan distances of each tile from its goal cell. Because a single slide can reduce this sum by at most one, the heuristic provides a lower bound on the number of moves required.
Parity of the permutation determines solvability; when the puzzle is solvable, the heuristic together with a parity correction gives a quick estimate of the minimum move count.
h = \sum_{i=1}^{N^2-1} \bigl(|x_i – x_i^*| + |y_i – y_i^*|\bigr)
h = sum of Manhattan distances for all tiles
Parameters
Result
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Frequently Asked Questions
What is a sliding puzzle?
A sliding puzzle is a game where numbered tiles are arranged in a grid with one empty space, and the goal is to reach a specific configuration by sliding the tiles.
How does the Manhattan distance heuristic work?
The Manhattan distance heuristic calculates the sum of the horizontal and vertical distances of each tile from its goal position, providing a lower bound on the number of moves needed to solve the puzzle.
What determines if a sliding puzzle is solvable?
A sliding puzzle is solvable if the parity of the permutation of the tiles is even. This means that an even number of inversions (tiles out of order) must exist for the puzzle to be solvable.
Can this calculator solve any size of sliding puzzle?
Yes, this calculator can handle N×N puzzles where N is at least 2. The most common sizes are 3×3 (8-puzzle) and 4×4 (15-puzzle).
What is the significance of the empty space in a sliding puzzle?
The empty space allows tiles to be moved around, enabling the player to rearrange the tiles to reach the goal configuration.
How does this calculator determine the minimum number of moves?
This calculator uses the Manhattan distance heuristic to estimate the minimum number of moves required to solve the puzzle by calculating the sum of distances each tile must travel to its correct position.
Can I use this calculator for a 5×5 sliding puzzle?
Yes, you can use this calculator for a 5×5 sliding puzzle. Simply input the current configuration of the tiles and the goal configuration to determine the minimum number of moves required.
Results are for informational purposes only and do not constitute professional advice.