Sudoku Cheat Sheet: Every Technique on One Page
This sudoku cheat sheet is built to be glanced at, not read. Every technique that appears in a normal puzzle is listed once, with two things beside it: the trigger — the exact thing you must see in the grid before the technique applies — and the action — what you're allowed to do once you've seen it. Nothing else. If you want a technique taught properly, follow its link; if you want to know what to try right now on the grid in front of you, stay on this page.
Print it, fold it, keep it under the puzzle. Everything below the master table is supporting detail you can ignore once the table is familiar.
The master table
Work top to bottom. The first technique whose trigger you can see is the one to use.
| # | Technique | Trigger — what you must see | Action — what you may do |
|---|---|---|---|
| 1 | Crosshatch | A digit already placed in rows/columns crossing a box, leaving one free cell | Place the digit there |
| 2 | Hidden single | A digit has only one possible cell in a row, column, or box | Place it |
| 3 | Naked single | A cell has exactly one candidate | Place it |
| 4 | Naked pair | Two cells in one unit hold the same two candidates | Erase those two digits from the rest of the unit |
| 5 | Naked triple | Three cells in one unit use only three digits between them | Erase those three digits from the rest of the unit |
| 6 | Hidden pair | Two digits appear in only two cells of a unit | Erase all other candidates from those two cells |
| 7 | Hidden triple | Three digits appear in only three cells of a unit | Erase all other candidates from those three cells |
| 8 | Pointing pair/triple | In one box, a digit's remaining cells all sit in one row or column | Erase that digit from the rest of that line, outside the box |
| 9 | Box/line reduction | In one row or column, a digit's remaining cells all sit in one box | Erase that digit from the rest of that box |
| 10 | X-Wing | A digit has exactly two cells in each of two rows, in the same two columns | Erase it from those two columns elsewhere |
| 11 | Swordfish | Same digit confined to three columns across three rows (2 or 3 cells each) | Erase it from those three columns elsewhere |
| 12 | Jellyfish | The same shape across four rows and four columns | Erase it from those four columns elsewhere |
| 13 | Skyscraper | A digit with two cells in each of two rows, sharing one column, not the other | Erase it from cells seeing both non-shared ends |
| 14 | Y-Wing / XY-Wing | Pivot cell AB; two pincers AC and BC, each seen by the pivot | Erase C from any cell seeing both pincers |
| 15 | XYZ-Wing | Pivot ABC; pincers AC and BC | Erase C from cells seeing all three |
| 16 | W-Wing | Two identical AB cells joined by a strong link on A | Erase B from cells seeing both |
| 17 | Simple coloring | One digit with exactly two cells in several units, chained together | Erase the digit where both colors are visible |
| 18 | Unique rectangle | Four cells in two rows, two columns, two boxes, sharing the same two candidates | Erase the extra candidate that would create two solutions |
| 19 | BUG+1 | Every unmarked cell is bi-value except one with three candidates | Place the digit that appears three times in its units |
Rows 1–9 solve the overwhelming majority of puzzles. Rows 10–19 exist for the days they don't.
How to read this sudoku cheat sheet
The order in the table is the order to try things in, because it's ranked by how much of the grid each technique makes you search.
A crosshatch looks at nine cells. A naked pair looks at one unit. An X-Wing compares two rows against two columns. A coloring chain can run through half the board. The logic doesn't get harder as you descend — an X-Wing is arguably simpler to justify than a hidden triple — but the searching does, and searching is where the time goes.
So: never reach for row 14 while a row 2 is sitting unfound. Whenever a technique fires and you place a digit, go straight back to row 1 and start again. Grids cascade, and one placement often makes four more trivial.
Notation, in one block
| Symbol | Meaning |
|---|---|
| RxCy | Row x, column y. R4C7 = row four, column seven |
| Row | One of nine horizontal lines of 9 cells |
| Column | One of nine vertical lines of 9 cells |
| Box | One of nine bold-outlined 3×3 blocks |
| Unit | Any row, column, or box — 27 in total |
| Peer | A cell sharing a unit with another. Every cell has exactly 20 |
| Candidate | A digit still legal in an empty cell (a pencil mark, not a rule) |
| Bi-value cell | A cell with exactly two candidates |
| Sees | Cell A "sees" cell B if they share a unit |
| Strong link | Two cells in a unit that are the only two homes for a digit |
| Given / clue | A digit printed at the start; it never changes |
Boxes are numbered 1–9 left to right, top to bottom, so box 1 is top-left and box 9 is bottom-right. The full statement of what makes a grid legal lives in sudoku rules.
Block 1: the singles
Triggers: a digit with one home, or a cell with one candidate. These produce most of every solve.
- Crosshatch. Choose a digit, look at a box, eliminate rows and columns where the digit already appears. One free cell left → place it. Best in the opening, before any marking.
- Hidden single. The digit is restricted. A 7 can only go in one cell of row 5, even though that cell also has candidates 2 and 9. Place the 7.
- Naked single. The cell is restricted. Only one candidate remains. Place it.
The difference between the last two is the most useful distinction on this sudoku cheat sheet. Naked singles jump out visually; hidden singles do not, and skipping them is the number-one cause of a stall that isn't really a stall. A walkthrough with a worked grid is in how to play sudoku.
Prerequisite for everything below: complete, current pencil marks. Half-marked grids generate false deductions.
Block 2: subsets
Triggers: n cells in a unit sharing exactly n digits (naked), or n digits confined to exactly n cells (hidden).
- Naked pair. R2C1 = {4,8} and R2C6 = {4,8}. Between them they own 4 and 8. Erase 4 and 8 from the other seven cells of row 2.
- Naked triple. Three cells using only {2,5,7} between them — and note they need not each hold all three. {2,5}, {5,7}, {2,7} is a valid naked triple.
- Hidden pair. In box 4, the digits 3 and 6 appear in only two cells. Those cells are 3 and 6. Erase everything else from them.
- Hidden triple. Same idea, three digits, three cells.
Hidden subsets are harder to see and more valuable, because they manufacture bi-value cells — the raw material every wing technique needs. Full treatment in naked pairs.
Block 3: locked candidates
Trigger: a digit's remaining cells in one unit all fall inside another unit that overlaps it.
- Pointing. Box 3's only cells for 9 are both in row 2. The 9 for box 3 must sit in row 2, so no other cell in row 2 can be 9. Erase 9 from row 2 outside box 3.
- Claiming (box/line reduction). Row 7's only cells for 4 are all inside box 8. So the 4 for box 8 lives in row 7. Erase 4 from box 8 outside row 7.
These are cheap to find and appear constantly. Per minute of study, they're the best value on the sheet. See locked candidate.
Block 4: fish
Trigger: one digit, confined to n columns across n rows (or vice versa).
| Fish | Rows/columns | How many cells per line | Frequency |
|---|---|---|---|
| X-Wing | 2 | Exactly 2 | Common on hard puzzles |
| Swordfish | 3 | 2 or 3 | Uncommon |
| Jellyfish | 4 | 2, 3, or 4 | Rare — usually skippable |
The search shortcut that saves the most time: only hunt fish among sparse digits. Count each digit's remaining candidate cells; anything with more than about nine is not worth scanning. See X-Wing and Swordfish.
Block 5: wings
Trigger: a small cluster of bi-value cells. No bi-value cells means no wings — skip the whole block.
- Y-Wing / XY-Wing. Pivot {A,B}, pincers {A,C} and {B,C}, each pincer seen by the pivot. Whichever value the pivot takes, one pincer becomes C. So erase C from every cell that sees both pincers. Details in XY-Wing and Y-Wing.
- XYZ-Wing. The pivot holds all three digits. Weaker: eliminations must see all three cells.
- Skyscraper. Two rows, one digit, two cells each, sharing exactly one column. Erase the digit from cells seeing both loose ends. See Skyscraper.
- W-Wing. Two cells with identical {A,B} candidates, connected by a strong link on A. Erase B from cells seeing both.
Block 6: chains and uniqueness
Trigger: everything above has failed on a grid you're confident is correct.
- Simple coloring. Take one digit. In every unit where it has exactly two possible cells, link those cells and alternate two colors. If one color appears twice in any unit, that color is false — place the other everywhere. If a cell sees both colors, the digit can't go there.
- Unique rectangle. Four cells in two rows, two columns, and exactly two boxes, all sharing the same two candidates, would give the puzzle two solutions. Since a well-formed puzzle has one, something must break the pattern. Erase accordingly.
- BUG+1. If every remaining unsolved cell is bi-value except one, that one cell takes the digit appearing three times among its units.
Uniqueness arguments assume the puzzle is well-formed rather than deducing from the grid alone, and some solvers decline to use them on principle. That's a legitimate position, not a mistake. More on the limits in sudoku expert, and on how these behave in practice in sudoku evil.
Triage card: the grid is stuck
| Symptom | Try |
|---|---|
| Several digits placed 6–8 times | Crosshatch those digits first |
| Units with 2–3 gaps | Hidden singles |
| Marks look messy or old | Re-mark the whole grid from scratch |
| Lots of 3–4 candidate cells | Hidden pairs and triples |
| A digit clustered in one line of a box | Pointing |
| A digit with under 9 candidate cells | X-Wing, then Swordfish |
| Four or more bi-value cells | Wings |
| A 2×2 pattern of matching pairs | Unique rectangle |
| Genuinely nothing, marks verified | Coloring — or take a break |
Triage card: the grid is broken
| Symptom | Meaning |
|---|---|
| A digit twice in one unit | A wrong placement upstream |
| A cell with zero candidates | Same |
| A digit with no home in a unit | Same |
| Two cells in a unit both forced to the same digit | Same |
None of these are fixable by more solving. Backtrack to a known-good state or restart. Do not attempt repairs — the arithmetic of the grid does not forgive.
Numbers worth memorizing
| Fact | Value |
|---|---|
| Cells in a grid | 81 |
| Units (rows + columns + boxes) | 27 |
| Peers per cell | 20 |
| Sum of any complete unit | 45 |
| Typical clue count | 22–35 |
| Minimum clues for a unique solution | 17 (proven by exhaustive computer search, 2012) |
| Number of valid completed grids | 6,670,903,752,021,072,936,960 |
The peer count is the one to internalize. Every digit you place constrains twenty other cells, which is why chasing the consequences of a placement pays better than continuing to scan.
Using it in practice
Keep the master table beside the grid for a week and you'll stop needing it — not because you memorized the table, but because the triggers become what your eye looks for. That's the actual point of a cheat sheet: it trains recognition, then becomes redundant.
For practice puzzles graded to a specific tier, the free generator at puzzlemakeronline.com will build and print sudoku at whatever difficulty you choose, so you can drill one block of this table at a time. And when you're ready to go from lookup table to structured learning, sudoku strategies lays out the same techniques as an ordered curriculum with a practice schedule.
Frequently asked questions
What should a sudoku cheat sheet actually contain?
The trigger and the action for each technique, ordered by search cost, plus notation and a stuck-grid triage list. Explanations belong in full articles; a cheat sheet's only job is helping you recognize what's in front of you and remember what it permits.
How many techniques do I really need?
Nine. Crosshatching, hidden and naked singles, naked and hidden subsets, pointing, box/line reduction, and X-Wing will finish nearly every newspaper and app puzzle. Everything past that is for puzzles built specifically to demand it.
Can I print this sudoku cheat sheet?
Yes — the master table plus the two triage cards fit on a single side of paper at a readable size. Those three tables are the parts worth having at the table; the rest is context you only need once.
Do I need pencil marks for all of these?
Everything from row 4 down requires complete, current candidate marks. The three single techniques don't, and on easy puzzles marking actively slows you down. Start marking at medium difficulty.
What's the difference between a naked and a hidden subset?
A naked subset is defined by the cells: n cells contain only n digits between them. A hidden subset is defined by the digits: n digits appear in only n cells. Naked ones are easier to see; hidden ones are more often the deduction you're missing.
Is using a cheat sheet cheating?
No. It lists what to look for, not where the digits go. Every deduction is still yours to find and justify. A reference that hands you answers would be a different thing entirely.