Sudoku Techniques for Beginners — Naked Singles, Hidden Singles, Pointing Pairs

Three logic techniques that solve most easy and medium Sudoku without guessing: the naked single, the hidden single, and the pointing pair, each with a worked example.

Most people who stall at Sudoku think the blocker is arithmetic. It is not. Sudoku uses no math at all — only the rule that each row, column and 3×3 box must contain the digits 1 to 9 exactly once. The skill is noticing where that rule leaves only one legal slot. Three techniques carry you through almost every easy and medium puzzle, and once you can spot them by eye you stop guessing entirely.

Why technique beats guessing

A well-made Sudoku has exactly one solution, and that solution can be reached by logic alone. When you guess, you risk painting yourself into a contradiction that you only discover twenty squares later. Techniques avoid that: each one is a small, airtight deduction that removes a candidate and tightens the board. Start with the two singles, then add the pointing pair, and most puzzles collapse on their own.

The naked single

A naked single is the simplest deduction: a square has only one candidate left, so that candidate must go there.

Imagine a square in the middle of a partially filled grid. Looking across its row you already see 1, 3, 4, 7 and 9. Looking down its column you see 2, 5 and 8. Looking inside its 3×3 box you see 6. The only digit missing from all three is the 1 — wait, that is eight digits accounted for, so the remaining one is whatever is not yet present. Say the row, column and box together rule out everything except the digit 6. Then that square is a naked single for 6, and you can place it with certainty.

The practical habit: after you fill any square, re-scan its row, column and box for other squares that just lost their last alternative. One placement often triggers two more.

The hidden single

A hidden single is the mirror image. A digit may have several open squares in a row, but only one of them is legal once you account for the columns and boxes.

Take the digit 4 in some row that still has three empty squares. At first glance 4 could go in any of them. But one of those squares shares a column with a 4 already placed elsewhere, and another shares a box with a 4. That leaves exactly one square in the row where 4 is still allowed — the hidden single. Even though the square had other candidates, the digit 4 has no other home in that row, so it goes there.

Hidden singles are easy to miss because the square looks "busy" with candidates. The trick is to hunt by digit, not by square: pick a number, and for each row, column and box ask "where can this digit still go?" When the answer is one place, you have found a hidden single.

The pointing pair

The pointing pair (and its cousin, the pointing triple) uses a box to eliminate candidates elsewhere.

Suppose a 3×3 box has two empty squares that could both hold the digit 5, and — crucially — both of those squares sit in the same column. Then the 5 for that box must land in one of those two squares, which means no other square in that column (outside the box) can be a 5. You have "pointed" the 5 out of the rest of the column and can erase it as a candidate there.

The same logic works in reverse across a row, and with three squares it becomes a pointing triple. The payoff is indirect: you are not placing the digit yet, you are removing a wrong option from somewhere else, which often turns a different square into a naked or hidden single.

How to combine them

The three techniques feed each other in a loop:

1. Scan for naked singles and place them.

2. Re-scan rows, columns and boxes for hidden singles by digit.

3. Look for pointing pairs that clear candidates elsewhere.

4. Return to step one — the board has changed.

Almost every puzzle labelled easy or medium falls to this loop plus patience. Notes (pencil marks) make it faster: writing the candidates in a square turns an invisible search into a visible one, so a pointing pair or a hidden single jumps out instead of hiding in your head.