Puzzle Cottage
Most Sudoku guides explain ten techniques in three paragraphs each and call it a day. The problem: when you’re actually stuck on a puzzle, you don’t need ten techniques — you need the right one for what you’re looking at. This guide covers the four techniques that solve 95% of all Sudoku puzzles, plus three more for Hard and Expert, with worked examples for every one. If you’re stuck right now, jump to what to do when stuck. If you’re a beginner, start with the rules.
How to play Sudoku for beginners (the rules in 60 seconds)
Sudoku is a 9×9 grid divided into nine 3×3 boxes. The grid starts partially filled with digits (the “clues”). Your job: fill in every empty cell so that:
- Each row contains the digits 1–9 exactly once.
- Each column contains the digits 1–9 exactly once.
- Each 3×3 box contains the digits 1–9 exactly once.
That’s it. The constraint is the whole game. Every cell’s value is forced by the row, column, and box it belongs to. There’s no math, no guessing, no luck — only logical deduction.
An example starting position — an Easy-difficulty puzzle:
A real Sudoku starting grid. Every empty cell has a unique correct value — finding them is the whole game.
What to do when you’re stuck on a Sudoku puzzle
Three things to try, in order. Most of the time the answer is the first one and you missed it.
- Re-scan for naked singles you missed. Pick a digit, walk every row/column/box. Half the time the “stuck” feeling is because you placed something incorrectly five moves ago and the cascade has gone wrong, or because there’s an obvious naked single you skipped.
- Pencil-mark every empty cell. If you haven’t already, write candidate digits in every empty cell. Tedious, but once you have a fully pencil-marked grid, harder techniques become mechanical.
- Step away for 10 minutes. Studies on cognitive incubation show that fresh eyes after a short break solve stuck problems faster than continuous staring. This is real, not folklore.
The one thing not to do: guess. Sudoku is deterministic — there’s always a logical next step. Guessing breaks the chain and almost always leads to a contradiction five steps later that forces a full restart.
Sudoku how to play step by step — the four core techniques
Technique 1: Scanning (naked singles)
Pick a digit — say 5. Find every row, column, and 3×3 box that already contains a 5. For each box without a 5, look at its empty cells: which ones could legally hold a 5 (no 5 in their row or column)? If exactly one cell qualifies, place the 5.
Worked example. The center 3×3 box below has no 5. Of its three empty cells, two are in rows that already contain a 5, so they’re blocked. Only the highlighted cell can hold the 5:
The green cell is forced to be 5 — it’s the only empty cell in the center 3×3 box where a 5 can legally go.
When to use: Always start here. Scanning alone solves most Easy puzzles and clears the groundwork for harder ones.
Technique 2: Pencil marks (candidate notation)
When scanning runs dry, start annotating. In each empty cell, write tiny candidate digits — every digit that could legally go there given current constraints.
This seems tedious, but with full pencil marks, the harder techniques (pairs, triples, X-wings) become almost mechanical. Puzzle Cottage Sudoku has a built-in pencil-mark mode — tap the pencil icon, then tap numbers to mark candidates.
Technique 3: Hidden singles
A hidden single is a digit that can only legally go in one cell within a row, column, or box — even if that cell has multiple candidates from other constraints.
Worked example. In a row with several empty cells, the digit 7 is needed. Three of those cells have a 7 already in their column or box (so 7 can’t go there). Only one cell remains where 7 could go — even though that cell’s pencil marks include {2, 4, 7}. The 7 is forced:
2 4
8 9
6 8
6 9
5 8
7 8
7
7 8
7 8
8
4 6
5
6
5 7
5 7
5 7
5 9
7 9
4 7
5 7
5 7
6 7
6 9
7 9
7 9
9
5 9
9
9
9
4 5
7
5
8
6 7
3
4 5
3 4 5 6
5 6 7
6
Top row: a hidden single. The 7 can only go in the rightmost empty cell of row 1 — every other empty cell in row 1 already has a 7 in its column or box. Hidden singles are the bread and butter of Medium Sudoku puzzles.
Technique 4: Naked pairs and hidden pairs
A naked pair: two cells in the same row, column, or box where both cells have exactly the same two-candidate pencil marks. Those two digits must split between those cells — so eliminate them from every other cell in the shared group.
A hidden pair: two candidates that appear only in two specific cells of a group (even if those cells have other candidates). Those two candidates lock the two cells — you can eliminate the other candidates from those cells.
Pairs are where Medium puzzles start to feel satisfying. Finding one is often the unlock for a 10-cell cascade.
Sudoku tips and tricks (intermediate)
Pointing pairs (box/line reduction)
If all candidates for a digit within a 3×3 box lie on a single row or column, that digit can be eliminated from the rest of that row or column outside the box. Niche-sounding, but it comes up every Hard puzzle.
Sudoku hidden triples examples
A hidden triple is the pair pattern extended to three. If three candidates appear only in three specific cells of a group (even if those cells have other candidates), those three candidates lock the three cells. Eliminate other candidates from them.
Hidden triples are uncommon but striking when they appear — one triple often unlocks 15+ cells worth of follow-up logic.
Sudoku X-wing examples
An X-wing is a pattern where a digit’s candidates in two rows are confined to the same two columns. Because that digit must occupy one cell in each row, those two columns can’t contain that digit anywhere else outside the X-wing.
Worked X-wing for digit 4:
- Row 2 has 4-candidates only in columns 3 and 7.
- Row 8 has 4-candidates only in columns 3 and 7.
- The 4 in row 2 is in either column 3 or column 7. Same for row 8.
- Whatever the assignment, columns 3 and 7 each get exactly one 4 from these two rows.
- Therefore: no other cell in column 3 or column 7 can be 4.
That’s the X-wing — eliminate 4 from every other cell in those two columns. The pattern works in either direction (rows confining columns, or columns confining rows). Required for some Hard puzzles, common on Expert.
Sudoku swordfish examples
Swordfish is X-wing extended to three rows. If a digit’s candidates in three rows are confined to the same three columns (each row using 2 or 3 of those columns), the digit can’t appear elsewhere in those three columns.
Swordfish is rare on standard Hard puzzles — you’ll see one maybe once a week if you play daily Hard. Recognizable by the “triangle of constraint” visual: three rows, three columns, the digit’s candidates form a 3×3 sub-grid you can think of as a tilted X-wing.
Sudoku XY-wing examples
XY-wing is a chain technique. Three cells with candidates {X,Y}, {Y,Z}, {X,Z} respectively, where the {Y,Z} cell sees both other cells. Whatever Y is, the chain forces Z out of every cell that sees both X-cells. Useful for Expert puzzles, rarely needed at Hard.
Sudoku examples with solutions: a worked Hard puzzle
The fastest way to internalize the techniques is to watch one applied end-to-end. We have a complete worked Hard puzzle on a past daily Sudoku — click into it and try the techniques in order: scan, pencil-mark, find pairs, look for X-wings. Most Hard puzzles use 4–6 of the techniques in this article.
When to give up and start over
Sometimes you’re stuck because you made a mistake earlier and the puzzle has gone unsolvable from your current state. Practical rule:
- Under 5 min stuck: keep going, re-scan.
- 5–15 min stuck: pencil-mark everything, look for pairs.
- Past 15 min stuck: probably a wrong placement earlier — restart, re-scan from scratch. The 30 seconds you save by not restarting are not worth the next hour of contradiction-chasing.
Are some Sudoku puzzles unsolvable?
A correctly-constructed Sudoku has exactly one solution — this is a definitional requirement, not just a goal. Generators that don’t check uniqueness can produce technically-valid grids with multiple solutions, but a 17+ clue puzzle from a reputable source is unique-solution by construction. Puzzle Cottage’s generator validates uniqueness before publishing.
If you’ve tried logic and reached a contradiction (a row needs two of the same digit, or a cell has zero candidates), you’ve made a mistake earlier. The puzzle isn’t broken — your placements are. Restart and re-scan.
The biggest mistake intermediate players make
Guessing. Never guess. Every time you feel the urge to “just try” a digit and see what happens, go back and pencil-mark more rigorously instead. Guessing leads to errors that cascade and force a full restart — and worse, it teaches you the wrong habits. Sudoku is a deterministic puzzle. Finding the next logical step is the whole game.