How to Solve Classic Sudoku on Paper with a Pen

A classic 9x9 Sudoku starts with roughly 27–30 givens and 81 digits to place. On screen, that sentence reads like a twelve-minute coffee-break puzzle. On paper with a pen, it is a full-immersion logic exercise — and this is the version that built the puzzle's reputation.

The method that follows is the three-pass workflow shared by the entire pen-and-paper Series Hub. Read that hub once for the general tools and notation systems; this guide applies them end-to-end on a single 9x9 board. If you need the theory behind the advanced patterns, pair this page with our X-Wing technique guide and the strategy index.

The two-pen rule: finals in blue, logic noise in red. The red pen is your eraser. When a candidate dies, strike it once instead of rubbing it out — you keep the audit trail and the page stays legible.

1. The Rules, Stated Precisely for Paper

• Place digits 1–9 so every row contains each digit exactly once.
• Place digits so every column contains each digit exactly once.
• Place digits so every 3x3 box contains each digit exactly once.
• A valid puzzle has exactly one complete solution — every deduction you make must agree with that single solution.

Because you cannot undo, treat each of these three "houses" as a separate ledger. A digit placed by row logic may violate the column — hence the constant 45-check during verification.

2. Notation You Need on One Sheet

Two systems cover 95% of classic boards. Corner notation for the early candidate phase, centre notation for resolved cells late in the solve.

3. Prepare the Workspace Before Pass One

4. Pass 1 — The Single Scan (Naked & Hidden Singles)

A naked single is a cell that accepts exactly one digit. A hidden single is a digit that fits in exactly one cell of a house. Both are found purely by scanning; that is why "scan first, mark later" saves time.

Repeat the sweep until no new singles fall out. At that point you have the board's "easy top layer". See the beginner tips guide for more scanning drills before moving on.

5. Pass 2 — Full Candidate Markup

For every remaining empty cell, write the candidate set — 1–9 minus the digits already in its row, column, and box. Work house by house (box by box is easiest) and keep digits tiny and grouped to the top-left. This is mechanical and boring. It is also the step that makes Pass 3 possible, and it is where paper solvers differ fundamentally from app players: there is no "auto-notes" here.

6. Pass 3 — Candidate Reduction Techniques

6.1 Naked Pairs

If two cells in one house share the exact same two candidates — say 3 and 8 — those digits are locked into those two cells. Strike 3 and 8 from every other cell in the house. Explained step-by-step in the naked pairs strategy page.

6.2 Hidden Pairs

Rarer, and easier to see with red pen: if two candidates appear in only two cells of a house (2 and 6, each only in R5C2 and R5C8), then those two cells must be 2 and 6 — strike every other candidate out of those cells. If that leaves a single surviving candidate in each, you've solved them. Details on the hidden pairs page.

6.3 Pointing Pairs

When a candidate appears only inside one row (or column) of a 3x3 box, that box is "pointing" at the rest of the row (or column): because the digit must live somewhere in the box, it cannot live anywhere else along that row/column outside the box. Strike accordingly.

6.4 Box/Line Reduction

The mirror image: when a candidate appears only within one box on a line, the digit is confined to that box entirely — strike it from adjacent boxes on that same line.

6.5 X-Wing and Swordfish

When row logic keeps failing, switch to fish patterns. An X-Wing is two rows where a candidate sits in exactly two cells each, and those cells align column-wise: the rectangle forces eliminations in the two shared columns. Swordfish is the nine-cell version. Practice diagrams live in the X-Wing guide and the Swordfish page. On paper, trace the rectangle in red pencil lightly first; commit the eliminations only when the corners close perfectly.

7. A Full Penalty-Free Board Walkthrough

The grid below is a real Medium board with givens in bold. The three red strike-throughs in Rows 5 and 7 are live eliminations made with pointing-pair logic on candidate 4 — the same pattern detailed in the X-Wing article.

Read the elimination this way: in the top-centre box, candidate 4 is confined to Column 4's cells. Because a 4 must land somewhere in that box, no other cell in Column 4 outside the box can hold a 4 — hence the three red strikes. That single reduction drops 6–8 candidates from the board and unlocks a chain of naked singles.

8. The Four Paper-Solving Mistakes That Kill Boards

• Restarting the scan early. Finish a full house-by-house sweep before flipping pens. Partial scans leave hidden singles undiscovered and bloat your candidate markup.
• Erasing candidates. Never erase. Strike through in red. Erased pages invite transcription errors, and once a strike is gone you lose the board's deduction history.
• Committing a digit with live candidates left. A placement is only safe when every other option at that cell has a strike. One un-struck candidate means the placement is a guess.
• Skipping the 45-check. The final audit catches column/box conflicts that row scanning misses — especially on boards where digits were placed through hidden pairs across boxes.

9. Train the Workflow, Then Carry It to Paper

Progression matters. Solve ten Easy boards strictly on paper, then Medium, then Hard, then Expert — and verify every finished grid with the 45-check. NetSudoku's boards are validated unique-solution puzzles, so a mismatch between your paper solve and the app's solution tells you precisely where the logic broke.

Classic 9x9 is the baseline every other puzzle in this series extends. When you can finish a Hard board with clean candidate notation and zero guesses, move to the Mini Sudoku guide to master instant-grid intuition, then explore the constraint-based variants.