Hidden pair

The naked pair seen from the other side. A naked pair is “two cells with only two digits”; a hidden pair is “two digits with only two cells”. Those cells have other candidates mixed in, so the pair does not show on the surface. Hence “hidden”.

Why it works

Say that in a row, the digit 6 can only go in cells A and B, and so can the digit 9. The row needs one 6 and one 9, so one of A and B is 6 and the other is 9. Those two cells are now spoken for, so every other candidate in A and B can be removed. Once you do, the two cells become an ordinary naked pair.

On a real board

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In row 7, 6 and 9 fit only in the two blue cells. So those cells can hold nothing else (red). Play this board →

This is a 9×9 · Expert board, filled as far as naked and hidden singles go. Candidates are shown for the empty cells of row 7.

In row 7, find the cells that have 6 as a candidate: only row 7, column 1 and row 7, column 9.
The digit 9 also appears in those two cells and nowhere else. That is a hidden pair.
The two cells must hold 6 and 9, so remove every other candidate from them (red).
One of the removed candidates was 2. As a result row 8, column 1 becomes 2, as a hidden single in column 1.

How it differs from a naked pair

	Naked pair	Hidden pair
You look at	Cells (with only two candidates)	Digits (with only two places)
The pattern	Two cells with the same two candidates	Two digits in the same two cells
You remove	The two digits from the other cells	Other digits from the two cells

In fact the two always come together within one line. If a line with five empty cells has a hidden pair, the other three cells form a naked triple, and either view removes the same candidates. People simply find whichever involves fewer cells easier to see.

Spotting it

In a line whose notes are complete, count for each digit how many cells it appears in. Two digits that each appear exactly twice, in the same two cells, make a hidden pair.
In Everydoku, tapping a cell with a digit highlights that digit everywhere, including in notes. Tap through the digits and ask “does this one appear only twice in this line?”.
Hidden triples work the same way: three digits confined to the same three cells clear every other candidate from those cells.

Where hidden pairs hide: in boxes with many empty cells and crowded notes. Each cell shows four or five candidates and nothing stands out, but counting by digit reveals two digits that appear in only two cells.

Where you need it

9×9 Expert and 16×16 Master boards have points where naked singles, hidden singles, locked candidates and naked pairs all get stuck. The hidden pair is one of the techniques most often used to get past them. Learn the X-Wing next as well.