Hidden pairs: keep two digits in their only cells

A hidden pair occurs when two digits can appear only in the same two cells of a unit. Keep those two digits in those cells and remove their other candidates; unlike a naked pair, the cells may initially contain extra notes.

Count positions for digits

Imagine a box where two and seven appear as candidates only in A and B. A currently has two, five and seven, while B has two, seven and nine. Other empty cells can contain five or nine, but none can contain two or seven.

The box still needs both two and seven. They must occupy A and B, so five disappears from A and nine disappears from B. The resulting notes form a naked pair, but the reason you found it was the restricted positions of the digits.

Inspect the full unit

Item	Candidate positions
two	A and B only
seven	A and B only
five	A and other cells
nine	B and other cells

The word “only” must include every empty cell. If a third cell C can contain seven, this particular hidden-pair proof is incomplete. Matching the visible notes in A and B is not enough.

Apply the reduction carefully

1. Pick a unit and list positions for each missing digit.
2. Find two digits sharing exactly the same two possible cells.
3. Recheck unmarked cells so that no legal location was overlooked.
4. Remove other candidates from the two reserved cells.
5. Revisit crossing units affected by those removals.

You are reducing the pair cells themselves. This is the reverse emphasis of a naked pair, where the two cells already have short candidate lists and you remove the pair digits from other cells.

Why this can reveal another deduction

Suppose A belongs to a column where five had been possible in A and one other cell D. Removing five from A forces five into D. Nothing in the hidden-pair argument directly named D, but the candidate update creates a hidden single in the crossing column.

This is why accurate notes matter across the board. A local reduction can travel through a crossing unit and produce a placement far from the original pair.

Check the near misses

Two digits confined to three cells are not a hidden pair. Three digits confined to two cells indicate a contradiction rather than a valid pair. A real pattern balances the number of required digits and the number of available homes.

Do not assume that every pattern must immediately place a digit. Preserving a smaller, correct candidate set is useful progress, even when the next deduction needs a fresh scan elsewhere.

Reduce a pair in a complete candidate snapshot

Here is a local example for a row whose missing digits are one, three, four, six and eight. Its other cells are already filled. Read every candidate list before searching for the two restricted digits.

Empty cell	Before reduction	After the hidden pair
A	one, three, six	three, six
B	one, four	one, four
C	three, four, six, eight	three, six
D	one, four, eight	one, four, eight
E	four, eight	four, eight

Three appears only at A and C. Six also appears only at A and C. The row requires both digits, and those are their only homes. Remove one from A and remove four and eight from C. Leave B, D and E unchanged by this deduction.

Notice that neither A nor C originally had just two candidates. Scanning only cells with two notes would miss this pair. Searching digit positions reveals it before the shorter candidate lists exist.

Carry one removal into a crossing column

Suppose C's column previously allowed eight only at C and another cell F. Once the hidden pair removes eight from C, F becomes that column's hidden single for eight. You can now place eight at F, although the original pair still has two possible arrangements.

1. Record three and six as the reserved digits for A and C.
2. Clear the unrelated notes inside those cells.
3. Check the crossing column for each removed digit; in this case eight now has only F.

Do not remove three or six from a remote cell just because it sees A. Either pair member might occupy A, so a crossing unit needs its own restriction before it can lose those candidates.

Break the pair deliberately

Add six to D's candidate list. Three still has only A and C, but six now has A, C and D. The shared two-position condition has disappeared, so C may still need four or eight. Restore the deleted notes if this was the actual board state. A hidden pair is about two complete position lists matching, rather than two cells sharing a few attractive digits.

Where to play

Open Ninefold when you want to practice turning crowded notes into smaller candidate sets. The iOS illustrated guides offer a refresher during play.