What is a hidden single in Sudoku?

A hidden single is a candidate number that can go in only one cell within a row, column, or box, even though that cell also holds other candidates. Because the digit has nowhere else to go in that house, it must be placed there.

What is the difference between a naked single and a hidden single?

A naked single is a cell with only one possible candidate left — you find it by looking at the cell. A hidden single is a cell that has several candidates, but one of those digits can appear nowhere else in the row, column, or box — you find it by looking at the digit. Naked singles are obvious; hidden singles are the ones players miss.

What is a hidden pair?

A hidden pair is two numbers that can only go in the same two cells of a house, even though those cells contain other candidates too. Once you spot a hidden pair, you can erase all the other candidates from those two cells, which usually turns them into a naked pair.

What is the difference between a naked pair and a hidden pair?

A naked pair is two cells that each contain exactly the same two candidates and nothing else — it lets you eliminate those two digits from the rest of the house. A hidden pair is two digits confined to the same two cells while those cells still show other candidates — it lets you eliminate everything else from within those two cells. Naked pairs clean up the house; hidden pairs clean up the cells.

What is a pointing pair in Sudoku?

A pointing pair is when all remaining candidates for a digit inside one box sit in the same row or column. Since the digit must go in that box, it must also be somewhere on that line, so you can eliminate the digit from the rest of that row or column outside the box.

Which technique should I learn first?

Learn hidden singles first. They require no pencil marks in simple cases, they appear in almost every puzzle, and they are the single most common reason a beginner gets stuck on a grid that is still solvable by scanning alone.

Naked & Hidden Singles and Pairs: The Sudoku Patterns That Unstick a Grid

Quick answer: A naked single is a cell with one candidate left. A hidden single is a digit that fits in only one cell of a row, column, or box, even if that cell shows other candidates. A naked pair is two cells holding the same two candidates. A hidden pair is two digits confined to the same two cells. Together these four patterns solve most medium puzzles.

Most beginners learn to hunt for naked patterns — cells that visibly have nothing else left. But the most common reason a player gets stuck is missing the hidden versions, which are sitting in plain sight behind a cluttered cell.

Here is the whole family, in the order you should learn them.

The four patterns at a glance

Pattern	What you look at	What it tells you	What you do
Naked single	One cell	Only one candidate remains	Place it
Hidden single	One digit in a house	It fits in only one cell	Place it
Naked pair	Two cells	Both hold the same two candidates	Erase those digits elsewhere in the house
Hidden pair	Two digits in a house	Both fit only in the same two cells	Erase all other candidates from those two cells

The word house just means a row, a column, or a 3x3 box — the three regions where the “1 to 9 exactly once” rule applies.

Notice the symmetry: naked patterns let you eliminate outside the cells you found, hidden patterns let you eliminate inside them.

Naked single

The simplest pattern. A cell has one candidate left, so that candidate is the answer.

You do not need pencil marks to find these early on — if a cell’s row, column, and box between them already contain eight distinct digits, the ninth belongs there. Once you are writing candidates, naked singles appear on their own as you eliminate.

Every placement you make can create new naked singles nearby, so after each one, glance at the neighbouring cells before moving on.

Hidden single

This is the highest-value pattern for a player leaving the beginner stage, and the one most often missed.

The trick is to focus on a digit, not a cell:

Pick a house — say a 3x3 box.
Choose a digit that is missing from it.
Count how many empty cells in that box could still legally accept that digit.
If the answer is exactly one, place it — even if that cell lists three other candidates.

Worked example. A box has four empty cells, and you are looking for where the 7 goes. Two of those cells sit in a row that already contains a 7 elsewhere on the grid. A third sits in a column that already has a 7. That leaves one cell. It does not matter that the cell also shows candidates 2, 4, and 7 — the 7 has nowhere else in the box to live, so the cell is a 7.

The digit is “hidden” because the cell looks busy. Players scanning for cells with one candidate walk straight past it.

Hidden singles hide in rows and columns too, not just boxes. When you get stuck, run this check for all nine digits across a few houses before reaching for anything more advanced.

Naked pair

Two cells in the same house contain exactly the same two candidates — say both show only {3, 8}.

You do not know which cell holds the 3 and which holds the 8. You do not need to. Between them, those two cells consume both digits, so no other cell in that house can be a 3 or an 8. Erase 3 and 8 from every other cell in the house.

The requirement is strict: each cell must show those two candidates and nothing else. A cell showing {3, 8, 5} does not qualify.

Hidden pair

The mirror image, and the harder one to see.

Two digits in a house can only go in the same two cells — but those cells also show other candidates.

Worked example. In one row, the digits 4 and 9 each appear as candidates in only two cells, and it is the same two cells both times. Cell A shows {1, 4, 6, 9} and cell B shows {4, 7, 9}.

Because 4 and 9 must occupy those two cells between them, nothing else can. Erase the 1, 6, and 7 — both cells collapse to {4, 9}, and you have converted a hidden pair into a naked pair. That naked pair may then let you eliminate 4s and 9s elsewhere in the house.

This two-step cascade is what makes hidden pairs so useful: they rarely place a digit directly, but they clear the clutter that was hiding everything else.

Pointing pairs

Worth knowing at the same time, because it uses the same reasoning across two houses at once.

Inside one box, all remaining candidates for a digit sit in the same row (or the same column). The digit must go somewhere in that box, so it must go somewhere on that line segment — which means it cannot appear anywhere else along that row outside the box. Eliminate it from the rest of the line.

Pointing pairs are the gateway to box/line reduction and the intermediate strategies that follow.

An efficient order to search

When a grid stalls, run this loop rather than staring:

Naked singles — quickest to spot, and each one changes the board.
Hidden singles, digit by digit, box by box. This resolves most stalls.
Naked pairs — scan for cells with exactly two candidates and look for a twin.
Hidden pairs — count candidate occurrences per digit within a house; any digit appearing in exactly two cells is worth checking.
Pointing pairs — check each box for a digit confined to one line.

Only if all five come up empty do you need the X-Wing and the techniques beyond it.

Common mistakes

Treating {3, 8, 5} as part of a naked pair. Naked patterns require exactly the two candidates, nothing more.

Forgetting that a hidden pair eliminates inward. After finding one, the other candidates in those two cells are gone — a lot of players spot the pair and then forget to do the erasing that makes it useful.

Only checking boxes. Hidden singles in rows and columns are just as common and easier to miss.

Not re-scanning after a placement. Every digit you place invalidates part of your candidate map. The pattern that was not there a minute ago may be there now.

Practice

These patterns are the bridge between basic crosshatching and genuinely hard puzzles — master them and most medium puzzles open right up, with hard becoming reachable.

Try them on a free puzzle, or print a page if you would rather annotate on paper.