How to Solve Sudoku: Complete Guide for Every Level

Sudoku is one of the most satisfying logic puzzles ever made — and one of the most misunderstood. Most people believe it requires mathematical skill or luck. It requires neither. Sudoku is pure deductive logic: every puzzle has exactly one solution, and every move can be proven correct before you write it in.

This guide takes you from the absolute basics through to advanced techniques used by expert solvers. Work through each section in order, or jump to the level where you feel challenged.

What Is Sudoku? Rules and Grid Setup

A standard Sudoku puzzle is played on a 9×9 grid, divided into nine 3×3 boxes (also called regions or blocks). The grid already contains some numbers — these are the given clues. Your job is to fill in every empty cell.

The one rule: Every row, every column, and every 3×3 box must contain each of the digits 1 through 9 exactly once.

That’s it. No arithmetic. No memory. Just logic.

Before you solve, learn to read the grid. The nine 3×3 boxes are usually referred to by position:

┌─────┬─────┬─────┐
│ NW  │  N  │ NE  │
├─────┼─────┼─────┤
│  W  │  C  │  E  │
├─────┼─────┼─────┤
│ SW  │  S  │ SE  │
└─────┴─────┴─────┘

Each row runs horizontally (9 rows), each column runs vertically (9 columns). A cell “sees” every other cell in its row, column, and box. The core insight of Sudoku is that if a digit already appears in a row, column, or box — it cannot appear again in any cell that sees those.

Beginner Techniques

Naked Singles (Last Remaining Digit)

A naked single is a cell that can only hold one possible digit. When every other digit from 1 to 9 already appears in that cell’s row, column, or box, the one remaining digit is the answer.

How to find them:

Pick an empty cell.
List every digit that appears in its row, column, and box.
If only one digit from 1–9 is missing from that combined list, write it in.

Example: A cell sits in Row 3, Column 7, inside the NE box. Row 3 contains 1,2,4,5,6,8. Column 7 contains 3,7,9. The NE box contains 2,4,9. Digits already eliminated: 1,2,3,4,5,6,7,8,9. Only 9 appears in both the column and box, and the row leaves 3,7,9 as gaps. Combining all: 1,2,3,4,5,6,7,8,9 — wait, let me simplify: if a cell’s row has 1,2,4,5,6,8 and its column has 3,7 and its box adds nothing new, the missing digits are {9} — so 9 is a naked single.

Most beginner puzzles can be solved entirely with naked singles and one more technique: hidden singles.

Hidden Singles

A hidden single is a digit that can only go in one cell within a row, column, or box — even if that cell has other possible digits.

How to find them:

For each digit 1–9, scan each row, column, and box:

Mark every cell where that digit could go (it doesn’t appear in the cell’s row, column, or box).
If only one cell is marked, place the digit there.

Example: In the top-left box, you need to place the digit 7. The box has four empty cells, but three of them lie in rows or columns that already have a 7. The fourth cell is the only one where 7 can go — even if that cell still has candidates 2, 4, 7. The 7 is “hidden” among those candidates. Place it.

Scanning

Before applying complex techniques, always scan the grid for easy wins:

Number scanning: For each digit 1–9, find how many times it already appears (it must appear 9 times in a solved grid). Digits that appear 7 or 8 times are almost complete — scan their remaining rows/columns/boxes to find the last one or two placements quickly.
Row/column/box scanning: Look for rows, columns, or boxes with only one or two empty cells. These are almost always naked singles.

Scanning takes 60–90 seconds and often gives you 5–15 free placements on a beginner puzzle.

Intermediate Techniques

Naked Pairs

A naked pair occurs when two cells in the same row, column, or box contain exactly the same two candidate digits — and no others. Those two digits must go in those two cells (in some order). Therefore, they can be eliminated from all other cells in that shared group.

Example: Cells A and B in the same row both have candidates {3, 8} and nothing else. You don’t know which is 3 and which is 8 yet — but you know for certain that 3 and 8 are “used up” in those two cells. Every other empty cell in that row can have 3 and 8 removed from their candidate lists.

Naked triples work the same way: three cells sharing the same three candidates (or any subsets of three candidates among three cells). Eliminate those three digits from the rest of the row/column/box.

Pointing Pairs (Locked Candidates Type 1)

If a candidate digit within a 3×3 box appears in only two or three cells, and all of those cells lie in the same row or column — then that digit cannot appear anywhere else in that row or column outside the box.

Why: The digit must go somewhere in the box. If it can only go in cells that share a row (or column), it will definitionally end up in that row (or column). So it cannot appear in any other cell in that row (or column) outside the current box.

How to use it: Remove that candidate from all cells in the same row/column that are outside the box. This often unlocks naked singles elsewhere.

Box-Line Reduction (Locked Candidates Type 2)

The reverse of pointing pairs. If a candidate digit appears in a row or column only within cells that all belong to the same 3×3 box, then that digit can be eliminated from all other cells in that box.

Why: The digit must end up somewhere in that row/column. If all viable positions are inside one box, the digit lands in that box — so it cannot appear in any other cell of that box.

Advanced Techniques

X-Wing

The X-Wing is the first technique that requires reasoning across multiple rows or columns simultaneously. It’s often the breakthrough technique that unlocks “hard” puzzle ratings.

The setup: Find a digit where, looking across all nine rows, it appears as a candidate in exactly two cells per row — and this happens in exactly two rows — and the two cells in each row share the same two columns.

Those four cells form a rectangle (the “X”). The digit must go in one diagonal of the rectangle or the other:

Either Row 1/Col A and Row 2/Col B, or
Row 1/Col B and Row 2/Col A.

In either case, columns A and B each get exactly one occurrence of the digit — in one of those two rows. Therefore, the digit can be eliminated from every other cell in columns A and B (outside those two rows).

How to find X-Wings:

Pick a digit (start with digits that appear 5–7 times already).
For each row, count how many cells it could go in. Mark rows where the count is exactly 2.
If two such rows share the same two candidate columns, you have an X-Wing.
Eliminate the digit from all other cells in those two columns.

Column-based X-Wings work identically: find two columns where the digit appears in exactly the same two rows, then eliminate the digit from all other cells in those two rows.

Swordfish

Swordfish is the three-row (or three-column) extension of X-Wing.

The setup: Find three rows where a candidate digit appears in exactly two or three cells per row. If those cells collectively span exactly three columns — and the columns are consistent across all three rows — the digit must go in one of those nine cells in a way that uses each column exactly once. Therefore, the digit can be eliminated from all other cells in those three columns.

Swordfish is rarer in standard puzzles but decisive when it appears. Look for it when X-Wing doesn’t yield results.

Y-Wing (XY-Wing)

Y-Wing uses a chain of three “bivalue” cells — cells with exactly two candidates each — to make a forced elimination.

The setup:

Find a pivot cell with candidates {A, B}.
Find two pincer cells, each sharing a house (row, col, or box) with the pivot:
- One pincer has candidates {A, C}.
- The other has candidates {B, C}.
The pivot forces a chain: if the pivot is A, the first pincer becomes C. If the pivot is B, the second pincer becomes C. Either way, one of the two pincers must contain C.
Therefore, any cell that sees both pincers (shares a row, column, or box with each of them) cannot contain C — it can be safely eliminated.

Y-Wing is particularly powerful because it doesn’t require the three cells to be in the same row, column, or box — they just need to share houses pairwise.

How to Approach a Daily Sudoku Puzzle

Every level of sudoku — easy through expert — responds to the same methodical approach:

Scan first (30–60 seconds). Count occurrences of each digit. Fill any naked singles you spot without pencilmarks.
Add pencilmarks (candidates) to all empty cells that remain. List every possible digit for each cell.
Apply naked/hidden singles across all rows, columns, and boxes. Update pencilmarks as you place digits.
Apply pointing pairs and box-line reduction. These two intermediate techniques knock out most “medium” puzzles.
Look for naked pairs/triples in rows, columns, and boxes. Remove candidates.
Apply X-Wing on any digit appearing as a candidate in many cells. Check all 9 digits.
Try Swordfish or Y-Wing if the puzzle remains stuck.

For “expert” or “diabolical” rated puzzles, you may need bifurcation (trial and error with systematic backtracking) — but most published daily puzzles are designed to be solvable with pure logic from the techniques above.

The calm, methodical approach — work through one technique category at a time, never guess, update pencilmarks after every placement — is also the most enjoyable. You stay in control of the logic at every step.

Frequently Asked Questions

Q: Can I solve Sudoku without pencilmarks?
For easy puzzles, yes — you can spot naked and hidden singles by eye. For anything harder, pencilmarks (small candidate digits written in each cell) are essential. They turn the puzzle from a memory task into a visible logic exercise.

Q: What is the hardest Sudoku technique?
Beyond X-Wing and Swordfish, the difficulty escalates rapidly. Jellyfish (4-row X-Wing), XYZ-Wing, chains (Alternating Inference Chains), and coloring are considered advanced. Most published “hard” daily puzzles only require up to Swordfish; expert puzzles may need simple chains.

Q: How many clues does a valid Sudoku need?
The minimum known is 17 clues for a uniquely-solvable puzzle. Most published puzzles give 22–30 clues; fewer clues generally (though not always) mean harder logic.

Q: Is Sudoku the same as a math puzzle?
No. The digits 1–9 could be replaced with any nine symbols (letters, shapes, colors). Only their distinctness matters, not their numerical values. There is no arithmetic in Sudoku.

Q: What does “daily Sudoku” mean?
A daily puzzle is a new puzzle released each day, the same for every player. It creates a shared ritual — you can compare solve times with others who played the same grid. Puzzmint releases a daily set including Sudoku, Nonogram, and region-placement logic — all solvable without ads or login.

What to Try Next

How to Solve Nonograms: Complete Guide — Master picture-logic puzzles with the overlap method and edge logic.
How to Solve Logic Grid Puzzles — Deduction chains and elimination grids explained step by step.
X-Wing Technique Explained (cluster article — coming soon) — Deep dive with worked examples.
Sudoku for Beginners: 5 Simple Rules (cluster article — coming soon) — Just starting out? Start here first.

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