How puzzles are made › Guide
How We Grade Logic Puzzle Difficulty
Solvedle grades one-star Star Battle by the deductions its logical solver uses, not just the grid's size. A weighted score describes the trace, while the published difficulty tier depends on the hardest technique and how often certain advanced techniques appear.
The score formula
Score = Σ (steps at level × level weight). This is a property of an implemented solving trace. A different deduction order or a stronger solver may produce a different trace for the same board.
| Level | Technique | Weight per step |
|---|---|---|
| 1 | Single candidate | 0 |
| 2 | Cell elimination | 0.15 |
| 3 | Two-unit confinement | 1 |
| 4 | Three-unit confinement | 2.5 |
| 5 | Four-unit confinement | 4 |
For example, one two-unit confinement and two cell-elimination steps score 1 × 1 + 2 × 0.15 = 1.3. Single-candidate placements still matter to the solve, but contribute zero to this particular score. Counting steps without their type would hide that distinction.
How are easy, medium, hard and expert assigned?
| Tier | Rule in the one-star grader |
|---|---|
| Easy | Hardest level is 1 or 2. |
| Medium | Hardest level is 3, used at most twice. |
| Hard | Level 3 used more than twice, or hardest level 4 used once. |
| Expert | Other solved traces: level 4 used more than once, or level 5. |
The score can rank traces within a band, but it is not the code that selects the tier. These statements concern the one-star grader. Tango and classic Takuzu have different technique systems; the two-star Classic label names its rule set rather than a calibrated difficulty level.
Does a larger board always mean a harder puzzle?
No. Size increases the number of cells to scan, but the required deduction can matter more than that search space. A larger board may unfold through single candidates, while a smaller one needs a region/row capacity argument. The historical generator results below illustrate overlap between sizes, not an experiment controlling size while holding clues constant.
| Grid | Easy | Medium | Hard | Expert | Accepted |
|---|---|---|---|---|---|
| 5×5 | 1732 | 211 | 0 | 0 | 1943 |
| 6×6 | 1434 | 310 | 11 | 0 | 1755 |
| 7×7 | 797 | 722 | 151 | 11 | 1681 |
| 8×8 | 565 | 791 | 293 | 43 | 1692 |
| 9×9 | 397 | 719 | 470 | 127 | 1713 |
| 10×10 | 298 | 602 | 534 | 271 | 1705 |
Each row counts accepted boards in that historical run; rejected attempts are not missing difficulty observations. For timing, methods, source revision and exclusions, use the original 12,000-seed report and its aggregate CSV. This table republishes that evidence; it is not a newly measured distribution of today's library.
What this score cannot tell us
- It is not a predicted solve time or population percentile.
- It does not prove that an alternative easier logical path is absent.
- It does not measure intelligence, learning gains or enjoyment.
- A larger score does not identify the move where real players abandon a board.
Player calibration needs a separate study with explicit denominators and sufficient samples. See what our present telemetry can measure. To experience the techniques, try Queens next-move checkpoints and counting proofs.
Implementation: one-star grade, score and tier functions. The article's weights are rebuilt from that score function and checked against it in tests.