Proven Sudoku
How difficulty is decided
Not by counting clues. By the hardest technique a solver actually needs.
The problem with counting clues
Clue count is the usual shortcut, and it is a bad one. Two boards with 30 clues each can sit at opposite ends of the difficulty range, because what makes a board hard is the chain of deductions it forces, not how much is filled in at the start. Grading by clue count is why one app's hard is another app's medium.
The ladder
Each level is generated against a ceiling: the hardest technique a solver is permitted to need. A board is only accepted at a level if it can be solved within that ceiling, and if it genuinely demands at least the level's floor. Without that floor a medium board could come out solvable by singles alone and feel identical to an easy one.
| Level | Needs at least | Never needs more than |
|---|---|---|
| Easy | Naked single | Hidden single |
| Medium | Locked candidates | Subsets (pairs and triples) |
| Hard | Subsets | X-Wing |
What "solvable by logic alone" means
It means a solver using only the techniques at or below the level's ceiling can fill every cell, without ever picking a candidate to try and backtracking if it fails. A puzzle that needs trial and error is not graded harder here. It is rejected and never published.
This also gives uniqueness for free. A deduction chain that never branches can only arrive at one answer, so every board has exactly one solution.
How it is checked
The check is not a spot check. Boards are generated deterministically from the date, which means the entire future schedule can be produced and verified ahead of time. Ten years of boards, three a day, is 10,950 puzzles, and every one of them was solved by the grader before any of them shipped.
Because generation is deterministic, this is reproducible rather than a promise: the same date always produces the same board, on every device and every platform.
What the audit actually found
Here is the measured result across all 10,950 boards, produced by re-deriving each board's hardest technique from the solver rather than trusting the value the generator recorded. Across every one of them:
- 0 boards could not be finished without guessing.
- 0 boards required a technique above the level's ceiling.
- 0 boards had more than one solution.
| Level | Hardest technique actually required | Clues |
|---|---|---|
| Easy | Naked single 96.8%, hidden single 3.2% | 40 |
| Medium | Locked candidates 73.9%, subset 26.0% | 31 to 32 |
| Hard | Subset 96.0%, X-Wing 3.9% | 25 to 28 |
Read the Hard row honestly: most hard boards are subset boards, and roughly one in twenty five needs an X-Wing. Anyone claiming every hard puzzle demands the exotic technique in their marketing is either not measuring, or not telling you.
None of this is a guess. Every number above comes from running the same check over all 10,950 boards, re-deriving each one from scratch rather than trusting the label the board was generated with.
What the app tells you
When you finish a board, it names the hardest technique that board actually required. Before you finish it says nothing, because naming the technique early would tell you what to look for, and that is a hint you did not ask for.
Where this can be wrong
Eight boards out of 10,950 came out easier than their floor. Four Medium boards need only singles, and four Hard boards stop at locked candidates. That is 0.073%, or roughly one board every fifteen months. They are still valid, still have exactly one solution, and still never need a guess. They are simply gentler than the level promises. The audit found them, and publishing the number is cheaper than pretending the floor is absolute.
The grader only knows the techniques listed above. A human solver who spots a pattern outside that set may find a board easier than its label suggests, and a solver who has not yet learned subsets will find Medium harder than the label implies.
The claim is deliberately narrow. No board requires more than its ceiling, none requires guessing, and every board has exactly one solution. That is a statement about the logic, not a promise about how hard a board will feel to any particular person on any particular morning.