T: technique
T_raw is the highest technique rank used. Rank 1 maps to 0 and rank 10 maps to 100.
Legen Difficulty Index v0
How Legen measures Sudoku difficulty.
The Legen Difficulty Index (LDI) is a 0–100 engine-relative score derived from the hardest verified technique, weighted logical work, and explicit candidate eliminations in a complete solve.
It is not a measure of intelligence, human completion time, or a universal ranking shared by every Sudoku solver.
Eligibility and scope
Only complete, verified logical solves receive a score.
A puzzle must have one solution, a non-empty proof trace, and a complete solve under the fixed ten-technique engine. Invalid, stalled, partial, and engine-error results receive no LDI.
Current engine order
Ranks 1–10 are fixed for this version. The engine selects the first canonical verified move in this order.
Raw facts and normalization
Three integer components become one 0–100 score.
Every component is recomputed from the verified trace. Calibration-only Q95 caps limit S and E before scaling; values above a cap remain 100.
S: weighted steps
S_raw sums rank − 1 for every logical step; it is scaled with the calibration Q95 cap.
S_cap = 32E: eliminations
E_raw counts candidate values explicitly removed by elimination proofs; it is scaled with the calibration Q95 cap.
E_cap = 14LDI = floor((4T + 3S + 2E + 4) / 9)T, S, and E use non-negative integer half-up scaling. The final formula adds 4 before integer floor, then stays within 0–100.
Frozen evidence
The reference corpus separates fitting from evaluation.
The 500 independent roots cover asymmetric and rotational source cohorts and are stratified by the hardest engine technique. Normalizers and thresholds use only the 400 calibration puzzles; the 100 locked holdout puzzles evaluate the frozen method.
Tier thresholds and observed counts
| Tier | LDI range | Calibration | Holdout |
|---|---|---|---|
| Easy | 0–14 | 119 | 23 |
| Medium | 15–21 | 83 | 24 |
| Hard | 22–35 | 98 | 32 |
| Expert | 36–100 | 100 | 21 |
Frozen evidence
Three calibration examples you can recompute
These examples come from the calibration split only. Apply the displayed caps and formula to reproduce each integer score and tier.
| Puzzle ID | Raw T / S / E | Normalized T / S / E | Score / tier |
|---|---|---|---|
LDI0-01cb0dcea7b0ea68bf57e4634a750ff0d862017f | 2 / 25 / 0 | 11 / 78 / 0 | 31 / Hard |
LDI0-01f7bd56a9d8bbbba1eda0ce28455ed0d638f233 | 2 / 9 / 0 | 11 / 28 / 0 | 14 / Easy |
LDI0-020a16dfa63d6d2cf42de1e946495f4d99bc3955 | 2 / 10 / 0 | 11 / 31 / 0 | 15 / Medium |
Clue count is descriptive, not a scoring input.
A puzzle with fewer given digits is not automatically harder. LDI records clue count in the public corpus, but the formula uses only verified T, S, and E.
Interpretation limits
Use LDI as a versioned engine description.
- The fixed solving order can choose one valid path when alternatives exist; another solver may take a different route.
- Technique strata with limited holdout coverage are marked sparse, so this version makes no stability claim for those ranks.
- LDI v0 uses no completion-time, hint, error, or other player-behavior data.
- Scores from different engine or LDI versions are not directly comparable and are never silently recalculated.
Sparse holdout ranks: Naked Single, Naked Pair, Hidden Pair, Naked Triple, Hidden Triple, X-Wing, XY-Wing, Swordfish.
Versions and corrections
The page and downloadable data are bound to frozen checksums.
- Method page updated
- Engine
legen-sudoku-engine/1.3.0- Analysis schema
legen-sudoku-analysis/v1- Algorithm
legen-ldi-algorithm/v0- Corpus
legen-ldi-reference-corpus/v0- LDI identity
legen-ldi/v0/sha256:f541ca7389fce1f8257d6051209f234ddcd83980c1834ea29c078e6af58e0dd7- Summary checksum
578c2eee75cb90a5f235feb2d290d68d7ce2bdc622e6dd569381516edecd442d- Public corpus manifest
d470beb77e228e01435a443563d1d38494e7149050538496a07ac3528110245d
Corrections are published with a dated note. Any change to bound data, scoring logic, thresholds, or engine fingerprints requires an explicit new version and fresh validation; historical scores are not silently rewritten.