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Hidden Pairs

Hidden pairs are the "dual" of naked pairs. They catch a pattern that's easy to miss, because the two candidates you care about are buried inside larger candidate lists in their cells. The payoff is the same: you can prune candidates aggressively, often opening the rest of a region up for quicker solving.

The Rule

A hidden pair occurs when two specific digits can appear in only two cells within a given unit (row, column, or box), even though those cells currently list several other candidates.

Because those two digits have nowhere else to go in the unit, the two cells together must hold exactly those two digits. Everything else in those cells' candidate lists can be deleted.

Worked Example

Consider a row with the following candidate lists:

Look at where the digits 4 and 6 can go. Scanning the row:

Both 4 and 6 are confined to the two cells A and C. That's a hidden pair on {4, 6}. Since A and C must together hold 4 and 6, every other candidate in A and C can be removed:

Notice what just happened: after the hidden pair was applied, cells A and C now look like a naked pair on {4, 6}. The two techniques are two sides of the same coin.

How to Find Hidden Pairs

  1. Pick a unit — a row, column, or box.
  2. For each digit 1 through 9, list the cells in that unit where the digit is still a candidate.
  3. Look for two digits that share the same two-cell list. If digit 4 can only go in cells A and C, and digit 6 can also only go in A and C, you've found a hidden pair.
  4. Reduce the candidate lists in those two cells to just those two digits.
  5. Re-scan. Hidden-pair reductions often create naked singles elsewhere.

Why They're "Hidden"

In a naked pair, the two cells advertise their candidates clearly — each cell has only two candidates, so you see the pair immediately. In a hidden pair, the two cells might have four or five candidates each; the pair only shows up if you change your perspective from "what can this cell hold?" to "where can this digit go?"

This shift in perspective — cell-first vs. digit-first — is a useful habit in general. Many intermediate and advanced techniques rely on the digit-first view.

Hidden Triples and Quads

Three digits that can each only appear in the same three cells of a unit form a hidden triple. Four digits in four cells form a hidden quad. The reasoning is identical: since those digits have nowhere else to go, those cells must hold exactly those digits, and all other candidates can be deleted.

Hidden triples and quads are rarer than pairs. They tend to show up in Hard and Expert puzzles, and are worth the occasional hunt once the obvious techniques have been exhausted.

Common Mistakes

When to Use Them

Hidden pairs typically enter the picture after scanning has run dry and you've placed some naked pairs. They're most common in Medium and Hard puzzles, and they show up often enough in Expert puzzles to be worth checking for during every stalled solve.

A good habit: when you feel stuck, pick a row, column, or box with many empty cells and run through digits 1–9 to see where each could go. More often than not, a hidden pair is the unlock.

Related Techniques

Practice

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Last reviewed on April 23, 2026.