Hidden Pairs in Sudoku: How to Spot and Use Them

A hidden pair is two digits that can only go in the same two cells of a row, column, or box. Those two cells must hold those two digits, so every other candidate in them can be erased. The pair is "hidden" because the two cells usually carry extra candidates that disguise it. Once you clear the extras, the hidden pair becomes a naked pair.

The rule

Pick a group: one row, one column, or one box. Look for two digits that each appear as a candidate in exactly two cells of that group, and in the same two cells. When you find them:

1. Those two cells must contain those two digits, in some order.
2. So no other digit can go in either cell. Erase all other candidates from both.

Note what does not change: the rest of the group. A hidden pair clears candidates inside the pair cells. A naked pair clears candidates from the other cells. People mix these up constantly, and it is the most common reason a hidden pair "doesn't work."

Worked example

Here is row 3 of a medium puzzle. It is missing 1, 2, 4, 6, 7, and 9, and the six empty cells have these pencil marks:

• R3C1: 1, 4, 6, 9
• R3C2: 1, 6
• R3C4: 2, 4, 7, 9
• R3C5: 1, 4, 6
• R3C7: 4, 6
• R3C9: 2, 4, 7, 9

Count where each missing digit can go. 1 fits in three cells. 4 fits in five. 6 fits in four. 9 fits in three. Now look at 2 and 7: each fits only in C4 and C9. That is a hidden pair. 2 and 7 must fill R3C4 and R3C9 between them.

So R3C4 and R3C9 cannot hold 4 or 9. Erase them, and both cells drop to {2, 7}. Now recount 9: it was possible in C1, C4, and C9, and only C1 is left. 9 is a hidden single in R3C1. One elimination turned into a placement, which is how hidden pairs usually pay off.

How to find hidden pairs

Count by digit, not by cell

Naked pairs jump out when you look at cells, because you see two cells with the same two marks. Hidden pairs only show up when you look at digits. For a single group, ask of each missing digit: how many cells can take it? Write the answer down or say it in your head. Any digit with exactly two spots is a pair candidate. If two such digits share the same two spots, you have a hidden pair.

Start with boxes that have many empty cells

Hidden pairs live in crowded groups, where cells have three or four candidates each and nothing looks resolved. A box with six or seven empty cells is a good place to run the digit count.

Use the pairs you already know

If you used pointing pairs or Snyder notation (marking a digit only when it has two spots in a box), you already know which digits are confined to two cells. Scan those notes for two digits sharing the same two cells. This is the fastest way to find hidden pairs in boxes.

Hidden pair vs naked pair

• Naked pair: two cells with only the same two candidates. Remove those two digits from the rest of the group.
• Hidden pair: two digits confined to the same two cells. Remove every other candidate from those two cells.

They are two views of the same fact. In any group with n empty cells, a naked pair in two cells implies a hidden set in the other n-2 cells, and the other way round. In practice, spot whichever one is easier to see in the group you are working on.

Where hidden pairs fit

Hidden pairs are a medium-to-hard technique. You reach for them after singles, pointing pairs, and naked pairs stop producing progress. The same idea scales up to hidden triples (three digits confined to three cells). Our complete list of sudoku techniques shows where each one sits.