Build candidates from constraints
Start with the digits 1 through 9, then eliminate every digit already visible in the cell’s three units. Suppose a cell’s row contains 1, 2, 4, and 8; its column contains 3 and 7; and its box contains 5. Only 6 and 9 remain, so the note should be {6, 9}. Do not add a candidate because it “looks likely.” Add it only because no rule currently excludes it.
Candidates describe the current state, not a permanent promise. When a peer receives a confirmed digit, that digit must be removed from the cell’s notes. Sudoku0 performs this peer cleanup after a correct placement, but you should still understand why the note disappeared.
Choose a notation style
Full notation records every legal candidate in every unsolved cell. It is systematic and especially useful for harder puzzles. Snyder notation records candidates mainly when a digit is limited to two cells inside one 3×3 box. It is faster and visually quieter, but it can be insufficient when you need row- or column-wide patterns.
Beginners usually benefit from full notation until candidate calculation becomes automatic. The important rule is consistency: switching styles unpredictably can make an incomplete note look like a real elimination.
Turn notes into deductions
A cell with one candidate is a naked single. A digit that appears as a candidate in only one cell of a row, column, or box is a hidden single. Candidate pairs can later support eliminations, and aligned candidates across boxes can create pointing-pair logic. Notes are therefore not administrative work; they are the raw material for patterns.
- Update peers immediately after every confirmed placement.
- Scan for one-candidate cells before searching for harder patterns.
- Scan each unit for a digit that appears in only one candidate list.
- Avoid deleting a candidate unless a unit constraint or a named pattern proves the elimination.
Prevent common note errors
The most damaging note error is treating incomplete notes as complete information. A pair such as {2, 7} matters only when you know those are the cell’s only candidates. Another mistake is leaving stale candidates after a placement. If the notes become unreliable, pause and rebuild the affected row, column, and box rather than continuing from a corrupted map.
Frequently asked questions
Should I write candidates in every empty cell?
For easy puzzles, selective notes may be enough. For difficult puzzles, full and consistently updated candidates make advanced patterns much easier to verify.
Is a two-candidate cell automatically a pair?
No. It becomes a useful naked pair only when another cell in the same unit has exactly the same two candidates.