Larsdoku¶

Pure logic Sudoku solver. Zero guessing. Every step proven.

Larsdoku solves the hardest Sudoku puzzles ever created using only logical deduction — no backtracking, no trial-and-error. Built on a bitwise engine with GF(2) linear algebra, it achieves 100% pure logic on the Top1465 benchmark (1,465 of the hardest known puzzles), averaging 19ms per puzzle.

At a Glance¶

Metric	Value
Top1465 solve rate	1465/1465 (100%)
Average solve time	0.019s
Max solve time	0.074s
Total techniques	20+ across 7 levels
WSRF inventions	4 (FPC, FPCE, D2B, FPF)
Dependencies	NumPy, Numba

Install¶

pip install larsdoku

Solve a puzzle in 3 lines¶

from larsdoku import solve

result = solve("4...3.......6..8..........1....5..9..8....6...7.2........1.27..5.3....4.9........")
print(f"Solved: {result['success']} in {result['n_steps']} steps")

Or from the command line¶

larsdoku "800000000003600000070090200050007000000045700000100030001000068008500010090000400" --board --no-oracle

Status: SOLVED
Steps:  63
Time:   26.0ms

┌───────┬───────┬───────┐
│ 4 6 8 │ 9 3 1 │ 5 2 7 │
│ 7 5 1 │ 6 2 4 │ 8 3 9 │
│ 3 9 2 │ 5 7 8 │ 4 6 1 │
├───────┼───────┼───────┤
│ 1 3 4 │ 7 5 6 │ 2 9 8 │
│ 2 8 9 │ 4 1 3 │ 6 7 5 │
│ 6 7 5 │ 2 8 9 │ 3 1 4 │
├───────┼───────┼───────┤
│ 8 4 6 │ 1 9 2 │ 7 5 3 │
│ 5 1 3 │ 8 6 7 │ 9 4 2 │
│ 9 2 7 │ 3 4 5 │ 1 8 6 │
└───────┴───────┴───────┘

What makes Larsdoku different?¶

Most Sudoku solvers fall back to guessing (backtracking) when they get stuck. Larsdoku never guesses. Instead, it escalates through increasingly powerful logical techniques until every cell is proven.

The solver pipeline:

L1 Singles → L2 GF(2) → L3 Fish → L4 Coloring → L5 FPC/FPCE → L6 D2B → L7 FPF

Each level fires only when everything above it has stalled. Four of these techniques — FPC, FPCE, D2B, and FPF — are original WSRF inventions not found in traditional Sudoku literature.

What is GF(2)?

GF(2) is Galois Field arithmetic (binary math). Larsdoku encodes Sudoku constraints as a system of linear equations over GF(2) and solves them using Block Lanczos decomposition. This finds forced digits that classical techniques miss — pure algebra, no search.