Sudoku Solving Techniques: From Beginner to Intermediate

1. Singles — The Foundation of All Solving

Most Sudoku puzzles yield to singles after other eliminations — placements where one cell must take exactly one digit. Before you hunt for clever patterns, build the habit of scanning for singles in rows, columns, and 3×3 boxes. Two ideas matter here:

• Naked Single — you look at a single cell and only one candidate remains.
• Hidden Single — you pick a digit and a unit (row, column, or box) and discover that digit can only fit in one cell, even if that cell still shows multiple pencil marks.

Singles are fast, reliable, and never guess. If you can see them consistently, Medium puzzles become comfortable and Hard puzzles become approachable.

A practical solving loop looks like this: fill every obvious single, then scan rows, then columns, then boxes, then repeat. Most players under-use Hidden Singles because they stare at individual cells instead of asking where a digit is still missing in the unit. Train both directions and you will cut your solve time dramatically.

Pencil marks matter. Naked techniques need an accurate candidate grid. On NewSudoku, toggle Notes mode to pencil in candidates, or update them mentally after each placement. Wrong pencil marks create phantom patterns; correct pencil marks make intermediate techniques feel automatic.

1.1 Naked Single

Difficulty: Beginner  ·  Also called: Sole Candidate

A Naked Single is the simplest logical move in Sudoku. Pick an empty cell, list which digits 1–9 are still possible after respecting every given and solved digit in its row, column, and box. If only one digit survives, place it.

How to spot it: After each placement, refresh candidates in the affected row, column, and box. Naked Singles often appear in clusters — solving one reveals the next. On easy puzzles you may complete entire regions using nothing else.

In the example below, cell B5 is empty while row B is otherwise filled except for that square. Existing digits in row B, column 5, and box 2 eliminate every candidate except 6. Notice that 6 may still appear as a candidate elsewhere in the row; that is fine. A Naked Single cares only about what is possible inside one cell.

Practise Naked Single on a generated puzzle→

Result: Place 6 in B5. Then update pencil marks in row B, column 5, and box 2 — new singles often appear immediately.

Common mistake: Confusing a Naked Single with a Hidden Single. If a cell shows only one pencil mark, it is naked. If a cell shows three pencil marks but digit 4 can only live there in the row, the logic is hidden. The placement is the same; the scan pattern is different.

1.2 Hidden Single

Difficulty: Beginner

A Hidden Single flips the viewpoint. Instead of asking “what can go in this cell?”, ask “where can this digit go in this row, column, or box?” Scan digit 1, then 2, up to 9. If a digit can only occupy one empty cell in a unit, that cell must take the digit — even when the cell still lists other candidates on paper.

How to spot it: Choose a unit and a digit. Cross out every cell where the digit is blocked by a given or solved number. If exactly one empty cell remains, you have a Hidden Single. This is especially useful in crowded boxes where no individual cell looks obvious.

Hidden Single in a box

In box 5 below, several cells are already solved. Check digit 7 across the box: D5 and F5 cannot take 7, and every other cell is filled. Only E5 still admits 7, so E5 must be 7.

Practise Hidden Single on a generated puzzle→

Result: Place 7 in E5.

Hidden Single in a row

Row C below has a single blank: C7. Scan digit 4 along the row. Each other cell is either filled or blocks 4 through its column or box peers. Only C7 can accept 4.

Result: Place 4 in C7. The same scan works column by column and box by box — that is why serious solvers rotate between units.

Hidden Singles in columns work identically: pick column 5, scan for digit 8, and mark every cell that still allows 8. When only one remains, place it. Many computer solvers try hidden singles in boxes first because boxes are visually compact, but human solvers often succeed faster along rows where empty cells line up horizontally.

International naming note: SudokuWiki and most English-language books call this technique Hidden Single. Older Russian tutorials sometimes label it "Last Hero" — the hero digit surviving every elimination inside a unit. The standard name is Hidden Single.

2. Naked Subsets — Eliminating Candidates

When singles stall, look for naked subsets. A group of n cells inside one row, column, or box contains exactly n candidates between them — no more, no less. Those digits are locked to those cells, so you may remove them from every other cell in the same unit.

Think of naked subsets as candidate accounting. If two cells in a row collectively own candidates {3, 7}, the row still needs a 3 and a 7 somewhere — and those two cells are the only owners. Every other cell in the row is pretending it might take 3 or 7; the pair forbids that.

Naked subsets can appear in rows, columns, or boxes. Boxes are often richest because eight related cells sit close together. After any elimination, re-scan the unit: removing candidates frequently exposes a new naked pair hiding in plain sight.

2.1 Naked Pair

Difficulty: Intermediate

A Naked Pair is two cells in the same unit that contain exactly the same two candidates — for example {2, 7}. Those digits must occupy those two cells in some order, so no other cell in the unit may keep 2 or 7.

How to spot it: Sort empty cells by candidate count. When two cells share an identical pair and nothing else, mark them. Then sweep the rest of the row, column, or box and erase both digits. Pairs are the workhorse of Medium puzzles.

In row A, A4 and A6 each show only {2, 7}. Cell A8 still lists {1, 2, 3, 7} and cell B5 in the same box still lists 2 and 7. Both digits are removed from those elimination cells.

Practise Naked Pair on a generated puzzle→

Result: Remove 2 and 7 from A8 and B5 (and any other affected cells in the row/box). A new single often appears immediately afterward.

2.2 Naked Triple

Difficulty: Intermediate

A Naked Triple is three cells in one unit whose candidates are drawn from exactly three digits — for example {2, 5, 9}. Cells may list two or three of those digits each; the rule is that together they never introduce a fourth possibility.

How to spot it: Look for three related cells in a row, column, or box where the union of candidates has size three. This is easier if you sort pencil marks and scan for overlapping small sets.

Row H below shows H2, H3, and H8 sharing {2, 5, 9}. Those digits cannot appear in any other empty cell of the row.

Practise Naked Triple on a generated puzzle→

Result: Strip 2, 5, and 9 from the remaining empty cells in row H.

2.3 Naked Quad

Difficulty: Intermediate (rare)

A Naked Quad extends the same idea to four cells and four digits. Quads are uncommon in human solving because pairs and triples usually appear first, but the logic is identical at larger scale.

How to spot it: When a row, column, or box has several cells with four or fewer candidates, check whether four cells together use exactly four digits. If so, eliminate those digits elsewhere in the unit.

Row E below uses a simplified teaching position: E1, E2, E8, and E9 share exactly {1, 4, 6, 8}.

Practise Naked Quad on a generated puzzle→

Result: Remove 1, 4, 6, and 8 from any other empty cells in row E.

3. Hidden Subsets — Revealing What Is Hidden

Hidden subsets are the mirror image of naked subsets. Instead of cells exposing the same candidates, a set of digits is confined to the same few cells inside a unit. Those cells may still show extra pencil marks, but the hidden digits leave no other home — so you trim the noise.

Hidden subsets feel slower at first because you track digits instead of glancing at cells. The payoff is huge on Expert puzzles where cells look crowded. A cell listing {2, 5, 8, 9} might secretly be a Hidden Pair cell after you discover 5 and 8 only appear there in the column.

Workflow tip: When a unit has only two or three empty cells left, switch to hidden logic immediately. Naked scans shine early; hidden scans finish the job when cells still show many candidates.

3.1 Hidden Pair

Difficulty: Intermediate

A Hidden Pair occurs when two digits appear as candidates in exactly two cells of a row, column, or box. Those two cells must therefore hold those digits, and every other candidate in those cells can be eliminated.

How to spot it: Pick a unit and scan digit by digit. Mark which cells still admit each digit. When two digits share exactly the same two cells, you have a Hidden Pair — even if those cells currently show four or five pencil marks.

In column 3, digits 4 and 8 only appear in D3 and G3. Strip the unrelated candidates from both cells.

Practise Hidden Pair on a generated puzzle→

Result: D3 becomes {4, 8} and G3 becomes {4, 8}.

3.2 Hidden Triple

Difficulty: Intermediate

A Hidden Triple is three digits that can only appear in three cells of a unit. After identifying the triple, each of those cells is reduced to the three digits involved (in whatever combination they already shared).

How to spot it: This is slower than finding a Hidden Pair because you are tracking three digits at once. Work box by box on harder puzzles; boxes concentrate candidates and make patterns visible.

In box 4, digits 2, 5, and 7 only occur in D1, D2, and E1. Extra candidates in those cells are removed.

Practise Hidden Triple on a generated puzzle→

Result: Each involved cell keeps only {2, 5, 7}.

3.3 Hidden Quad

Difficulty: Intermediate (rare)

A Hidden Quad is four digits restricted to four cells in a unit. Like the naked version, quads are rare but occasionally unlock a stuck region.

How to spot it: Use the same digit-tracking method as Hidden Pairs, but look for four digits sharing exactly four cells. Software helpers call this often; human solvers may see it only a few times per puzzle, if at all.

Row F below demonstrates digits 1, 3, 6, and 9 confined to four cells.

Practise Hidden Quad on a generated puzzle→

Result: Involved cells are trimmed to the quad digits only.

4. Intersections — Rows, Columns, and Boxes

Intersection techniques (also called Locked Candidates) exploit overlap between a 3×3 box and a row or column. They are the bridge from subset logic to the advanced fish patterns you will meet later. Andrew Stuart's SudokuWiki groups them under Intersection Removal; HoDoKu and many apps split them into two directional rules.

Naming ambiguity to know: English sources disagree on labels. Pointing Pair/Triple (SudokuWiki, HoDoKu) describes box → line eliminations. Claiming or Box/Line Reduction describes line → box eliminations. Some older books say Locked Candidates Type 1 (pointing) and Type 2 (claiming). The logic is identical worldwide; only the direction name changes.

Always ask two questions when a box and row intersect: (1) Are all copies of a digit in the box lined up on one row? (2) Are all copies of a digit on the row trapped inside one box? One yes answer produces eliminations.

4.1 Pointing Pair / Pointing Triple (Locked Candidates Type 1)

Difficulty: Intermediate  ·  Also called: Pointing Pair, Pointing Triple, Box-Line Interaction (Type 1)

Look inside a single box. If every candidate for a digit lies on one shared row or column inside that box, the digit cannot also appear on that row or column outside the box. The pair or triple inside the box "points" along the line and eliminates candidates.

How to spot it: Choose a box and scan digit by digit. When all instances of a digit line up on one row or column, extend your gaze along that line beyond the box and remove the digit.

In box 2, digit 5 appears only in A4 and A5 on row A. Therefore 5 cannot appear in A1, A2, or A3 outside the box.

Practise Pointing Pair on a generated puzzle→

Result: Remove 5 from A1, A2, and A3.

4.2 Box/Line Reduction (Locked Candidates Type 2)

Difficulty: Intermediate  ·  Also called: Claiming, Box-Line Reduction, Line-Box Reduction

Box/Line Reduction is the reverse direction. Scan a row or column. If every candidate for a digit inside that line lies within one single box, the digit cannot appear elsewhere in the same box outside the line.

How to spot it: After updating pencil marks, pick a row and scan each digit. If candidates are confined to one box intersection, sweep the rest of that box and eliminate the digit. Repeat for columns.

In row A, digit 2 only appears in A4 and A5, both inside box 2. Remove 2 from the other empty cells of box 2: B4, B5, C4, and C5.

Practise Box/Line Reduction on a generated puzzle→

Result: Remove 2 from B4, B5, C4, and C5.

5. What's Next

You now have the full beginner-to-intermediate toolkit used by NewSudoku's hint engine up through Hard and Expert puzzles. The next tier looks for contradictions across several rows and columns at once instead of inside one unit, and each pattern has its own page with a trainer: X-Wing, Swordfish, XY-Wing and alternating inference chains.

The best way to internalize today's techniques is deliberate practice: play a Medium puzzle on newsudoku.app, enable pencil marks, and before tapping Hint ask yourself which technique should fire. When the hint matches your guess, you are reading the board correctly.

Suggested training path: Week one — singles only on Easy and Medium. Week two — add naked pairs and pointing pairs on Hard. Week three — hidden pairs and box/line reduction on Expert. Week four — mix all eleven techniques without hints, using hints only to verify stalemates. By then, fish patterns in Part 2 will make sense because you already reason about lines and boxes overlapping.

In short: an X-Wing finds a digit forming a rectangle across two rows and two columns; Swordfish generalizes that rectangle to three lines; an XY-Wing chains three bivalue cells to eliminate a digit from a shared peer. Each builds on the candidate discipline you practiced here, and each has a drill of its own in the technique trainer.

Glossary

Naked Single

Only one candidate remains in a single cell.

Hidden Single

A digit can only be placed in one cell of a row, column, or box.

Naked Pair / Triple / Quad

N cells in a unit share exactly N candidates; those digits leave other cells in the unit.

Hidden Pair / Triple / Quad

N digits in a unit are confined to N cells; other candidates are removed from those cells.

Pointing Pair / Triple

All candidates for a digit in a box line up on one row or column; eliminate the digit along that line outside the box.

Box/Line Reduction

All candidates for a digit in a row or column lie in one box; eliminate the digit from the rest of the box.

Locked Candidates

Umbrella term for pointing (Type 1) and claiming / box-line (Type 2) intersection moves.

Candidate / Pencil mark

A small note showing a digit might still fit in a cell.

Unit

Any row, column, or 3×3 box.