Hidden pairs: two digits, two cells

Hidden pairs belong to the same family as naked pairs, but they are harder to see. You do not look for two cells with matching candidates. You look for two digits that have only two possible places in a unit. Once you spot them, the two cells can be cleared of everything else.

What is a hidden pair?

A hidden pair is two digits that are possible in only the same two cells of a row, column or box. Those two digits must occupy those two cells, so the two cells can hold nothing else. Every other candidate in them can be removed, even when the cells look full of notes.

How it works

1. Pick a unit with several empty cells.
2. For each missing digit, list the cells in the unit where it is still possible.
3. Look for two digits whose lists are the same two cells.
4. Remove every other candidate from those two cells. The two digits stay.

The picture below shows box 1, the top-left box. The digits 4 and 7 can only go in the two cells marked x.

Row 2 holds a 4 at r2c5 and a 7 at r2c9. Those cells block the other two empty cells of box 1 in row 2, which are r2c1 and r2c2 (marked -). The only remaining cells for 4 and 7 in box 1 are r1c1 and r3c3. Those two cells hold the hidden pair. Any candidates in them other than 4 and 7, such as 8 and 9, can be removed.

How to spot it

• Work from the digits, not the cells. For a unit, count the places for each missing digit. A digit with exactly two places is the start of a hidden pair.
• Look for two such digits sharing a pair of cells. If digit A and digit B both have the same two places, you have a hidden pair.
• Expect busy cells. Hidden pairs are usually found in cells with three or more candidates, because the extra digits are what you remove. Use notes and highlights to see every copy of a digit at once.
• Check after singles. Hidden pairs often appear once the easy singles are done, because each placement removes possible places for other digits.

Hidden pairs and naked pairs compared

Both techniques remove candidates from two cells, but they look different on the board.

A worked example

The next picture shows row 5, the middle row of the grid.

Row 5 has four givens: 1, 2, 4 and 5. The missing digits are 3, 6, 7, 8 and 9, and the empty cells are r5c4, r5c5, r5c7, r5c8 and r5c9. Now check where 3 and 9 can go.

• Digit 3. Column 5 has a 3 at r1c5, so r5c5 is out. Column 7 has a 3 at r2c7, so r5c7 is out. Column 9 has a 3 at r8c9, so r5c9 is out. That leaves r5c4 and r5c8.
• Digit 9. Column 5 has a 9 at r8c5, column 7 has a 9 at r7c7, and column 9 has a 9 at r1c9. Those rule out the same three cells, so again only r5c4 and r5c8 are left.

The two digits 3 and 9 are a hidden pair in r5c4 and r5c8. Suppose both cells show the candidates {3, 6, 7, 8, 9} at the moment. The pair removes 6, 7 and 8 from both. Each cell is left with {3, 9}, and the digits 3 and 9 stay in them.

Common mistakes

• Looking only for matching lists. That finds naked pairs. A hidden pair is about two digits whose places match, not two cells whose candidates match.
• Removing the pair digits from the pair cells. The digits 3 and 9 remain in r5c4 and r5c8. Only the other candidates go.
• Missing a blocker. Before you claim a pair, check that the two digits really have no other place in the unit. One forgotten copy of a digit can make the pair false.
• Giving up on busy cells. Many players skip cells that have lots of notes. Those cells are often where hidden pairs are hiding.

Building the habit

Hidden pairs reward patience more than cleverness. The most useful habit is to work through one digit at a time: for a unit, list the places for each missing digit, then compare the lists. Two digits with identical two-cell lists are a hidden pair. This method is slower than scanning for matching candidates, but it finds pairs that other methods miss.

It helps to check hidden pairs after you have finished the singles and locked candidates in a region. Each of those steps removes possible places, which often reduces a digit to exactly two cells. A grid that looked stuck can open up once the hidden pair is found.

If you want the basics before you start, how to solve sudoku covers the rules and singles from scratch, and the Learn hub lists the full sequence of techniques. Hidden pairs are part of what Hush’s Medium level asks you to master, and the Hush home page shows how the levels fit together.

Practice hidden pairs in Hush

Hidden pairs appear in Hush’s Medium level, together with locked candidates and naked pairs. Medium puzzles are unlimited and free, and the daily puzzle is a Medium puzzle from Monday to Thursday, so you can practice often. If the naked version is the one you find easier, go back to naked pairs first. When you are ready for three or four digits at once, read triples and quads. For the technique that comes before pairs, see locked candidates. If you like playing without interruptions, offline sudoku explains how every Hush puzzle ships with the app.