Sudoku Academy — Free Techniques, Singles to X-Wing

Everything you need to go from complete beginner to confident solver.

How Sudoku Works

Sudoku is a logic puzzle played on a 9×9 grid divided into nine 3×3 boxes. The goal is simple: fill every cell so that each row, each column, and each 3×3 box contains the digits 1 through 9 exactly once.

Each row, column, and 3×3 box must contain digits 1–9 exactly once.

The key rule: No number can appear twice in the same row, column, or box. Every valid Sudoku has exactly one solution — there is no guessing involved in a well-formed puzzle.

Solving Your First Puzzle

When you pick up a new puzzle, follow this four-step approach:

Scan the givens

Look at which numbers already appear in each row, column, and box. This tells you what's missing and where candidates can go.

Find obvious singles

Look for a cell where only one digit is possible, or a digit that can only go in one cell within a row/column/box. Place it.

Write pencil marks

For cells that aren't immediately obvious, note the possible candidates in small writing. As you fill cells, eliminate candidates from related cells.

Repeat and eliminate

After placing each digit, rescan affected rows, columns, and boxes. A chain reaction often reveals several new cells at once.

Never guess. If you're unsure, it means you're missing a logical deduction — not that you should try random numbers. Scan again, look for a new angle.

How to Train

The fastest way to improve is deliberate practice — not just solving puzzles, but solving them in a way that builds specific skills.

Beginner

Only naked and hidden singles needed (SE 1.2). In matches 28–40 clues — the fullest grids for your first games. Build speed and scanning habits here first.

Start here

Intermediate

Mostly 27–33 clues — the logic is what gets harder (SE 1.5–2.3): pairs, pointing techniques, and box-line reductions.

When you're consistent

Expert

Mostly 27–33 clues, but much harder logic (SE 2.5–4.8): chains, wings, fish patterns, and advanced eliminations.

Advanced players

Time trials

Race yourself. Solve the same difficulty puzzle repeatedly and track your personal best times.

Speed training

Use Solo sudoku on Sudoku Corner to solve puzzles without time pressure or ELO stakes. Review every puzzle you get wrong — understanding your mistakes is more valuable than moving on quickly.

Tips to Become a Better Player

Always scan all three constraints

For each unfilled cell, always check its row, its column, and its 3×3 box simultaneously. Most beginners only look at one.

Use pencil marks systematically

Fill in all possible candidates for every empty cell before you start solving. This gives you the full picture and prevents missed eliminations.

Work on the most constrained cells first

Cells or regions with the fewest candidates are the easiest to solve. Always pick the cell with the least options — it gives the most information.

After each placement, immediately update

When you place a digit, instantly remove it from all pencil marks in the same row, column, and box. Don't wait — stale candidates mislead you.

Learn one technique at a time

Don't jump to X-Wings before you've mastered pairs. Each technique builds on the last. The section below covers them in order of difficulty.

Practice speed separately from accuracy

First aim for zero errors. Once you can solve cleanly, start tracking time. Speed comes from pattern recognition built through repetition — not rushing.

Solving Techniques

These techniques are listed from easiest to most advanced. Master them in order — each one builds on the previous. Every technique also has its own in-depth guide with step-by-step spotting instructions and practice puzzles taken from real rated games:

Naked Single Beginner Hidden Single Beginner Naked Pair Intermediate Hidden Pair Intermediate Pointing Pair Intermediate Claiming Intermediate Naked Triple Intermediate X-Wing Expert Swordfish Expert XY-Wing Expert Unique Rectangle Expert Forcing Chain Expert Nishio Expert Sue de Coq Expert

Easy

Naked Single

The simplest move in Sudoku. A cell has only one candidate left — so it must be that digit.

1Pick any empty cell and look at its row, column, and 3×3 box.

2List which digits 1–9 are already placed anywhere in that row, column, or box.

3If exactly one digit is not in that list, it must go in this cell. Place it.

4After placing, rescan all cells in the same row, column, and box — another naked single may have appeared.

Tip: Beginners often check only one constraint (e.g. just the box). Always check all three — row, column, and box — at the same time.

The centre cell's row, column, and box together already contain 1,2,3,4,6,7,8,9 — so 5 is the only option.

Easy

Hidden Single

A digit that can only go in one cell within a row, column, or box — even if that cell appears to have several candidates. The single is "hidden" among other possibilities in that cell.

1Pick a digit (e.g. 7) and pick a unit — a row, column, or box — where it isn't placed yet.

2Go through every empty cell in that unit. For each one, check: does 7 already appear in its row, column, or another constraint? If yes, 7 is blocked there.

3If only one cell in the unit is not blocked, then 7 must go there — regardless of what other candidates that cell has.

4Place 7 and continue. Remove it as a candidate from all cells sharing a row, column, or box with the newly placed cell.

Tip: Scan each digit 1–9 systematically across all rows, then all columns, then all boxes. Hidden singles are the most common technique in beginner puzzles.

7 is blocked in all cells except one — place it there, even if that cell has other candidates too.

Intermediate

Naked Pair

Two cells in the same unit each contain exactly the same two candidates and nothing else. Those two digits are "reserved" for those two cells — you don't know which goes where yet, but you can eliminate both from every other cell in the unit.

1Fill in pencil marks for all empty cells. Look for a row, column, or box with two cells that each contain only the same two digits — for example, both cells show only {3, 7}.

2Confirm: both cells must have exactly those two candidates — no other digits. If one cell has {3, 7, 9}, it's not a naked pair.

3Since 3 and 7 must go into those two cells (one each), they cannot go anywhere else in the unit. Remove 3 and 7 from the pencil marks of all other cells in the same row/column/box.

4After eliminating, check if any other cell in the unit now has only one candidate — that would be a naked single you can place immediately.

Tip: A naked pair can also span a column or a box — not just a row. Always check all three unit types.

Both blue cells contain only {3,7} — remove 3 and 7 from all red cells in the same row.

Intermediate

Pointing Pair / Triple

Inside a 3×3 box, a candidate sometimes only appears in cells that all share the same row (or column). Since that digit must go somewhere in the box, it must land in that row — so you can eliminate it from the rest of that row outside the box.

1For a given digit, look at all its possible positions inside one 3×3 box.

2Check: do all those positions fall within the same row? (Or the same column?) If yes, you have a pointing pair or triple.

3Because the digit must land somewhere in that box, and all candidates in the box are in that one row, it will definitely end up in that row.

4Remove that digit as a candidate from all other cells in the same row that are outside the box. Those cells can no longer contain it.

Tip: This works the same way vertically — if all candidates for a digit in a box are in the same column, eliminate it from the rest of that column.

Digit 2 can only go in the middle row of the left box → eliminate 2 from the rest of that row in other boxes.

Intermediate

Naked Triple

Three cells in the same unit that together hold only three distinct candidates (distributed across those cells). Those three digits are "reserved" for those three cells and can be removed from all other cells in the unit.

1Fill in all pencil marks. Look for three cells in a unit whose candidates together form a set of exactly three digits. For example: {1,4}, {1,4,9}, {4,9} — together they only use 1, 4, and 9.

2Each individual cell doesn't need all three — one cell may have {1,4}, another {4,9}, another {1,9}. What matters is that the union of all three cells' candidates has exactly 3 digits.

3Confirm no fourth digit appears in any of the three cells. If it does, it's not a naked triple.

4Remove those three digits (1, 4, 9 in the example) from the pencil marks of all other cells in the same unit. Look for new naked singles that may emerge.

Tip: Naked triples are easy to miss because the three cells don't all look the same. Train yourself to look at the combined set of candidates across a group of cells.

Green cells collectively use only {1,4,9} — remove those digits from all other cells in the row.

Advanced

X-Wing

A pattern spanning two rows and two columns. When a candidate is locked into the same two columns in two different rows, those four cells form a rectangle — and the candidate can be eliminated everywhere else in those two columns.

1Find a digit that appears as a candidate in exactly two cells in one row. Note the column positions of those two cells.

2Search for another row where the same digit also appears in exactly two cells, and crucially, in the same two columns.

3You now have four cells forming a rectangle. The digit must go in one of the two "diagonal" combinations — either top-left + bottom-right, or top-right + bottom-left. Either way, it occupies exactly one cell per column.

4This means the digit cannot appear anywhere else in those two columns. Eliminate it from all other cells in both columns.

Tip: X-Wing also works by scanning columns first — find two columns where a digit appears in exactly two cells in the same two rows, then eliminate from those rows.

Digit 5 locked to the same two columns in two rows → eliminate 5 from all other cells in those columns.

Advanced

Y-Wing (XY-Wing)

A chain of three bi-value cells (cells with exactly two candidates). The logic forces one specific digit out of any cell that "sees" both end cells of the chain.

1Find a cell with exactly two candidates — call them A and B. This is your pivot.

2Find a second bi-value cell that shares a unit (row/col/box) with the pivot and contains A and a third digit C. This is Pincer 1.

3Find a third bi-value cell that shares a unit with the pivot and contains B and C. This is Pincer 2. (Pincer 2 does not need to share a unit with Pincer 1.)

4Reason: if the pivot is A → Pincer 1 must be C. If the pivot is B → Pincer 2 must be C. One of these is always true.

5Therefore: any cell that sees both pincers simultaneously can never contain C — eliminate C from those cells.

Tip: The two pincers don't need to share a unit with each other — only each one with the pivot. The eliminated cells are those seen by both pincers at once.

Pivot forces C into one of its pincers — any cell visible to both pincers can never be C.

Expert

Swordfish

Swordfish is X-Wing extended to three rows and three columns. When a candidate appears in 2 or 3 cells in each of three rows, and all those cells collectively span only three columns, the candidate is locked within those rows/columns and can be eliminated from the rest of those columns.

1Find three rows where a particular digit appears as a candidate in exactly 2 or 3 cells per row.

2Check all the column positions of those candidates across all three rows. If they collectively occupy only 3 distinct columns (not 4, not 5 — exactly 3), you have a Swordfish.

3The logic: the digit must be placed once in each of the three rows. No matter how it's distributed across the three columns, it will cover each of those three columns exactly once.

4Eliminate the digit from all other cells in those three columns — any cell in those columns that is not part of the Swordfish pattern cannot contain the digit.

Tip: Like X-Wing, Swordfish also works column-first. This is a rare but powerful technique — spotting it in a real puzzle is very satisfying.

Digit 6 in 3 rows spans only 3 columns — eliminate 6 from all other cells in those three columns.