Hidden Pairs and Triples in Sudoku

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 you can erase every other candidate from them. The pair is "hidden" because the cells still show other candidates until you clean them up.

It's the mirror image of a naked pair. A naked pair clears digits out of the rest of the unit. A hidden pair clears other digits out of the pair itself.

An example

Look at a single row, and suppose your notes show:

• Cell A: {1, 3, 6, 8}
• Cell B: {3, 5, 8}
• No other cell in the row has a 3 or an 8 as a candidate.

The row needs a 3 and an 8, and the only places they can go are A and B. So A and B are the 3 and the 8, in some order. That leaves no room for anything else in those cells: erase 1 and 6 from A, and 5 from B. Both cells become {3, 8}, which is now a naked pair.

Hidden triples

Same logic with three digits and three cells. If 2, 4 and 9 can only go in the same three cells of a box, those cells hold 2, 4 and 9, and you can erase every other candidate from them.

As with naked triples, each digit doesn't have to appear in all three cells. What matters is that every candidate for 2, 4 and 9 in the unit sits inside those three cells and nowhere else.

How to spot them

Hidden subsets are harder to see than naked ones because the cells look busy. The trick is to count by digit instead of by cell:

1. Pick a unit that's still fairly empty, like a box with five or six open cells.
2. For each missing digit, count where it can go in that unit. Write it down if you need to: "3: A, B. 8: A, B. 6: A, C, D."
3. Look for two digits with the same two cells. That's your hidden pair.
4. Clean the cells, then check the rest of the unit. The new naked pair may knock candidates out of other cells.

Naked or hidden: which to look for?

In a crowded unit with few open cells, naked pairs are easier to see. In an open unit with lots of empty cells, hidden pairs are often the better bet, because a naked set would need many cells while the hidden set needs only two or three digits.

Practice

Try the Hidden Pairs lesson, then Subsets: Mixed Practice, which mixes naked and hidden sets. Then take a Hard puzzle from the play page and look for hidden pairs in the emptiest boxes.