Difficulty

Every genre rates puzzles by the human techniques they need, on one shared scale. The engine is described in the framework design, and each genre lists its techniques on its own page.

Terms

• Rule instance: one place a rule applies, such as a row, a 2x2 block or an island’s number.

• Technique: a named, sound deduction that a solver can spot and explain, with a level and an order in the genre’s profile.

• Bookkeeping: routine consequences of values already written in, such as removing a placed digit from its row. It is applied but does not count toward a rating’s level or techniques.

• Broken: candidates that can no longer satisfy every rule.

Levels

Level	Meaning
Easy	Direct deductions from a single rule or clue.
Medium	Standard combinations and small local patterns.
Hard	Larger patterns, or short “if this cell were X, a rule would break” chains.
Expert	Combinations of several patterns, and longer chains.
Extreme	Reserved. No genre generates it yet.

Levels are skill bands within a genre. An easy sudoku and an easy nurikabe need not take the same time.

Genre	Easy	Medium	Hard	Expert
Fillomino	wall-offs, single exits, room counting, enclosed pairs	cells a region needs, ways to finish a region, small pockets, immediate rule breaks	contradiction chains of up to 6 steps	up to 20 steps
Hashi	island bounds, isolated pairs	only connections, immediate rule breaks	contradiction chains of up to 6 steps	up to 20 steps
Hitori	sandwiches, pairs, corners, cut cells	two rounds of routine consequences breaking a rule	contradiction chains of up to 6 steps	up to 20 steps
Kakurasu	weight bounds	short lists of combinations	long lists, contradiction chains of up to 6 steps	up to 20 steps
Kakuro	sum combinations, singles, a digit with one place in a run	combinations that fit the candidates of a run	contradiction chains of up to 6 steps	up to 20 steps
Nurikabe	separating numbers, pools, single exits	unreachable cells, immediate rule breaks	contradiction chains of up to 6 steps	up to 20 steps
Sudoku	singles	pointing, claiming, naked pairs	hidden pairs, triples, quads	fish, wings, kites, coloring, X- and XY-chains

Rating procedure

Code and tests cite these rules by number.

L1-L2. Variables and literals. A genre’s candidates are a mask per variable (at most 16 values). A literal names one value of one variable in the genre’s answer format.

L14. Canonical solving. From the printed puzzle, the solver repeatedly applies the first step of the first technique, in the profile’s order, that makes progress. Bookkeeping comes first. A puzzle’s level is the level of the hardest technique on this path. The level is exact for this rater version; a person using other strategies may find a puzzle easier or harder.

L15-L16. Determinism. Optimizations must not change results, and a budget that runs out is an error. A deduction cannot depend on randomness, a time limit, the solution or an assumption that the puzzle is unique.

L17-L18. Score. The score is the total size of the step explanations. It changes between rater versions and does not estimate solving time. Ratings can also include research metrics, which may change in any version.

Rating results

L19-L20. A puzzle is rated only after the genre’s brute-force solver proves it has exactly one solution. If the techniques cannot finish a unique puzzle, rate returns an “unrated” error. Each step records its technique, level, removed candidates, the candidates it relies on and the earlier steps that established them. Hints give the first skill step after bookkeeping and do not use the solution.

Generating by difficulty

L21. A puzzle generated at a requested level has exactly that rating. With no level requested, any level from easy to expert is accepted.

L22. Changing an internal search limit changes the generator version. Attempt limits, work budgets and cancellation can make generation fail, and when it succeeds the puzzle is the same under any of them.

L24/V3. Changes that affect ratings or generated puzzles bump the rater or generator version, and the code for the old version is deleted. A seed reproduces a puzzle within one generator version, so puzzles are shared by ID.