The logical baseline
Before assigning a level, Sudoku Pilot checks that the starting clues lead to exactly one solution. Its solver must then complete the grid with the same named techniques available in the coach. The rating and solve metadata must remain stable when the check runs again.
The solver tests technique groups in order. Singles produce Easy or Medium puzzles, with a 45-step cutoff between them. Pointing and Claiming Candidates extend the ceiling to Hard. Pairs, triples, and quadruples extend it to Expert. Fish, wings, colouring, Crane, and Empty Rectangle extend it to Extreme. The first group that completes the puzzle sets its level.
The one-move problem
A technique ceiling tells us what the solver needed. It says less about how much of the puzzle depended on that technique. A long solve may contain one X-Wing followed by a large run of singles. The X-Wing makes the rating Extreme even when the advanced part is brief.
Our previous Extreme catalog showed this clearly. On the recorded deterministic paths, 84 of its 100 puzzles had one Extreme-level unblocking moment. The remaining 16 had two. The labels correctly described the technique ceiling, while the collection offered too little sustained advanced work.
Counting hard gates
For an Expert puzzle, the solver applies every available technique through Hard. If the grid remains unsolved, an Expert subset move is required, so the solver counts one hard gate. It applies that move, exhausts the easier techniques again, and repeats.
Extreme uses the same process after exhausting every technique through Expert. If no easier move appears after a gate, the next Extreme move counts as another gate immediately. Every Expert and Extreme catalog puzzle now needs at least five gates on its certified path.
This is a deterministic path metric. It describes the stable move order used for certification. Another valid solving order may use fewer gates. Searching every possible move order grows expensive quickly, so we record the path we can reproduce and avoid claiming a mathematical minimum.
Why good puzzles are rare
A valid Sudoku grid is easy to generate. A good puzzle at a specific level is much rarer. It needs one solution, a complete path through supported techniques, and enough hard gates to feel consistently Expert or Extreme.
Adding a correct clue gives the solver more information, so it preserves or simplifies the logical path. It cannot create the richer chain of deductions we need. Our search removes clues or swaps them for other correct clues, then runs the rating and uniqueness checks again.
Most attempts fail those checks. In one recent run, 161 of 4,743 Expert attempts qualified, about 3%. For Extreme, 240 of 27,477 qualified, less than 1%. The rest landed at another level, lacked five gates, needed unsupported techniques, had uneven clue layouts, or repeated puzzle structure we already had.
Choosing for variety
Five gates sets the quality floor. A whole set can still feel repetitive when the same hard move appears at the same point in every solve. Final selection spreads clue counts, total solve steps, gate positions, and tier-level techniques.
Canonical identity checks remove puzzles that only relabel digits or rearrange the same structure. We also limit how many selected puzzles may descend from one starting grid.
Taste remains subjective. Some players enjoy several related deductions in a row. Others prefer long stretches of easier progress between hard moments. The rating gives us a repeatable standard, and the diversity checks prevent one kind of solve from dominating the catalog.