Solving techniques

By Multiplayer Sudoku · Updated

The short answer

Four techniques solve almost every sudoku: scan one digit at a time across the grid, place naked singles (cells with only one remaining candidate), find hidden singles (digits with only one possible home in a row, column or box), and keep pencil marks current so the harder patterns reveal themselves.

Every sudoku can be solved by logic alone — the difference between difficulties is which logic. These four techniques, learned in order, carry you from your first easy grid to expert territory. (New to the rules? Start with how to play.)

1 · SCANNING

Take one digit — say 7 — and sweep the grid. Every placed 7 forbids its whole row and column, so in many boxes only one cell can still take a 7. This 'cross-hatching' fills surprisingly much of an easy grid before you think hard at all.

2 · NAKED SINGLES

Look at one cell and ask what it can still be. If its row, column and box already contain eight different digits, only one candidate is left — a naked single. It's forced; place it and ride the chain reaction.

3 · HIDDEN SINGLES

Flip the question: inside one box (or row, or column), where can the 4 go? If every cell but one is blocked, the 4 is hidden there — even when that cell has other candidates written in. Hidden singles crack most medium grids.

4 · PENCIL-MARK DISCIPLINE

From hard difficulty up, keep candidates written in every empty cell (auto-notes does the initial sweep here). The advanced patterns — pairs, triples, pointing candidates — are all things you notice in the pencil marks, not in the big numbers.

Beyond singles

When singles run out, these techniques take over. Learn them in this order, from the simplest to the most advanced:

  1. 5Pointing pairsA digit locked to one line inside a box clears the rest of that line.
  2. 6Naked pairsTwo cells that can only hold the same two digits clear those digits from their unit.
  3. 7Hidden pairsTwo digits with only the same two homes clear every other candidate from those cells.
  4. 8X-WingOne digit, two rows, the same two columns: clear the digit from the rest of those columns.
  5. 9SwordfishOne digit, three rows, the same three columns: clear the digit from the rest of those columns.
  6. 10SkyscraperOne digit, two rows with two spots each, one end lined up: clear the digit from cells that see both other ends.
  7. 112-String KiteOne digit, a row and a column with two spots each, joined in a box: clear the digit where both far ends meet.
  8. 12XY-WingThree two-option cells, a pivot and two pincers: whatever the pivot is, one pincer is z.
  9. 13Empty RectangleA box where the digit forms an L or a cross, plus one strong link: clear the cell where they meet.
  10. 14XYZ-WingLike an XY-Wing, but the pivot can be z too: clear z from the cells that see all three.
  11. 15W-WingTwo cells that can only be x or y, bridged by x: one of them is y.
  12. 16Unique RectangleFour corners that could swap two digits would mean two solutions; a proper sudoku has one.
  13. 17Simple ColoringFollow one digit through its strong links in two colors: exactly one color is true.
  14. 18X-ChainFollow one digit through alternating links: one end of the chain must hold it.
  15. 19XY-ChainA chain of two-option cells: if the first isn't z, the last one is.

When a grid stalls

Stuck grids are almost never actually stuck — a candidate somewhere is wrong or missing. Re-scan your most recent placements before hunting exotic patterns; nine times out of ten a plain single was hiding behind a stale pencil mark. If you'd rather keep momentum, a hint here points out a cell that has exactly one candidate — it teaches the same habit the techniques do.

Techniques, multiplied

Co-op mode is quietly the best trainer: one player scans while another chases singles, and you see each other's reasoning land on the shared grid in real time. Bad candidates get caught faster with four eyes on the board.

Theory done. Practice time.

PLAY SOLO

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