generatedAt string | engine string | rows list |
|---|---|---|
2026-09-13T14:16:23.653Z | LKSlide IDA* (Manhattan + linear conflict) | [
{
"board": "3x3",
"mode": "optimal (W=1)",
"scrambleDepth": 10,
"games": 200,
"meanMoves": 9.6,
"medianMoves": 10,
"meanNodes": 22,
"medianNodes": 18
},
{
"board": "3x3",
"mode": "optimal (W=1)",
"scrambleDepth": 20,
"games": 200,
"meanMoves": 17.2,
"media... |
Sliding Puzzle Solver Benchmark — Solution Length & Search Nodes
Optimal (and near-optimal) solution length and search effort for the LK Forge Sliding Puzzle Solver, which uses IDA* with a Manhattan-distance + linear-conflict heuristic. The 8-puzzle (3×3) is solved optimally (weight = 1); the 15-puzzle (4×4) uses a lightly-weighted, near-optimal search. Boards are generated by a seeded random walk of the blank from the goal.
- How the solver works: https://lkforge.com/tools/puzzles/sliding-puzzle-solver/how-the-sliding-puzzle-solver-works.html
- Try it: https://lkforge.com/tools/puzzles/sliding-puzzle-solver/
- Producer: LK Forge — client-side AI games, solvers, and tools.
Headline numbers
8-puzzle (3×3), optimal, 200 boards per scramble depth:
| Scramble depth | Mean optimal moves | Mean search nodes |
|---|---|---|
| 10 | 9.6 | 22 |
| 20 | 17.2 | 353 |
| 30 | 20.2 | 962 |
| 40 | 21.6 | 1,373 |
| 50 | 21.4 | 1,500 |
Past 40 random moves the board is effectively fully scrambled and the optimal solution length
converges to ~22 moves — matching the known average optimal solution length of the 8-puzzle
(21.97 over all solvable states). Search nodes plateau because the state is already random.
15-puzzle (4×4), near-optimal autoSolve, 200-move scrambles: mean 53 moves, ~232k nodes.
Files
data/sliding-puzzle-benchmark.json— per board size / scramble depth: mean & median moves and search nodes.
Method
- Engine: the shipped
sliding-solver-engine.js(LKSlide), used unmodified. - Node = one IDA* expansion (machine-independent measure of search effort).
- Boards generated by seeded random walk (always solvable), verified with the parity test.
Reproduce
node scripts/benchmark-sliding-puzzle.mjs
Citation
LK Forge (2026). Sliding Puzzle Solver Benchmark — Solution Length & Search Nodes. https://lkforge.com/tools/puzzles/sliding-puzzle-solver/
Everything runs client-side, no login, no tracking.
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