Sudoku Hidden Pairs and Hidden Triples, Explained

Once you know naked pairs, the next step is hidden pairs. They use the same idea, two digits locked into two cells, but they are harder to see because other candidates "hide" them. This guide explains how they work and how to find them. You will need candidate notes (pencil marks) in your grid.

New to candidates? Start with our beginner techniques guide.

Quick reminder: naked pairs

A naked pair is two cells in the same row, column or box that contain only the same two candidates, like {2, 9} and {2, 9}. Those two digits must go in those two cells, so you remove 2 and 9 from the rest of the unit.

What is a hidden pair?

A hidden pair looks at the problem from the other direction. Instead of asking "which digits can go in these cells?", it asks "where can these digits go in this unit?"

If two digits can each appear in only the same two cells within a row, column or box, then those two cells must contain those two digits. Any other candidates in those two cells can be removed.

Example

Imagine a row where, after checking candidates:

• The digit 4 can only go in cell A or cell B.
• The digit 7 can only go in cell A or cell B.
• Cell A's candidates are {1, 4, 6, 7}.
• Cell B's candidates are {3, 4, 7, 8}.

Because 4 and 7 have nowhere else to go in this row, cells A and B must hold 4 and 7 (in some order). That means 1 and 6 can be erased from cell A, and 3 and 8 can be erased from cell B.

After the cleanup:

• Cell A: {4, 7}
• Cell B: {4, 7}

You now have a visible (naked) pair, and erasing those other candidates often creates new singles elsewhere.

How to find hidden pairs

Scanning cells will not reveal hidden pairs, because the cells look busy. Instead, scan digits:

1. Pick a row, column or box.
2. For each digit from 1 to 9 that is not yet placed, count how many cells it could go in.
3. Write down the digits that have exactly two possible cells.
4. If two of those digits share the same two cells, you have a hidden pair.

Highlighting tools in Sudoku apps make this much faster: highlight one digit and see where it appears in each unit.

Hidden triples

The same logic extends to three digits. If three digits can only appear in the same three cells in a unit (not every cell needs all three digits, but together the three digits are confined to those three cells), then those cells must contain those digits. Remove all other candidates from the three cells.

Hidden triples are rarer and harder to spot. Look for them after you have checked for hidden pairs.

Common mistakes

• One of the digits has a third possible cell. Then it is not a hidden pair. Both digits must be limited to exactly the same two cells.
• Mixing units. All the cells must be in the same row, column or box.
• Removing from the wrong cells. With hidden pairs, you remove other candidates from the pair cells themselves, not from the rest of the unit. (With naked pairs, it is the other way around.)

Where hidden pairs fit in your solving order

1. Cross-hatching and singles.
2. Naked pairs.
3. Pointing pairs.
4. Hidden pairs, then hidden triples.
5. X-Wing and other advanced patterns.

Hidden pairs are one of the most useful medium-level techniques. Once you get used to scanning by digit instead of by cell, you will start finding them quickly.