Hidden Pairs in Sudoku

What is a Hidden Pair?

A Hidden Pair happens when two digits can only be placed in the same two cells within a row, column, or 3x3 box — even though those two cells also have other candidates marked. The pair is "hidden" because extra candidate noise makes the lock invisible at first glance.

Once you find the pair, you can erase all other candidates from those two cells. The two digits are locked in — they have nowhere else to go in the unit, so no other digit can sit there either.

Hidden Pair vs. Naked Pair (the key difference)

Beginners often mix these up. Here is the cleanest way to remember:

• Naked Pair — scan by cell: find two cells whose only candidates are the same two digits. The lock is on the cells.
• Hidden Pair — scan by digit: find two digits that each have only the same two possible cells in a unit. The lock is on the digits.

Both end with the same two-cells-two-digits structure. The difference is which side of the equation gives it away first. Naked Pairs jump out from a quick cell scan. Hidden Pairs require you to think about digit placement.

Why it works (the logic)

Suppose in one row, digit 4 can only go in cells R1C2 and R1C5. Suppose also that digit 7 can only go in the same two cells, R1C2 and R1C5.

One of those cells must hold 4, and the other must hold 7. That leaves zero room for any other digit in either cell — even if the pencil marks currently list 1, 3, 8, or anything else as a candidate there.

So you can confidently erase every candidate except 4 and 7 from R1C2 and R1C5. Often this single cleanup triggers a chain of Naked Singles, Hidden Singles, or fresh Naked Pairs.

Example 1: Hidden Pair in a row

Consider Row 5 below. Suppose 3, 5, and 8 are already placed in this row. You scan the candidates and notice:

• Digit 1 can only go in cells R5C2 and R5C7 — every other cell in row 5 already sees a 1.
• Digit 6 can only go in cells R5C2 and R5C7 — same situation.
• But R5C2 also has pencil marks {1, 4, 6, 9}, and R5C7 has {1, 2, 6, 7}. The pair is hidden under those extra candidates.

Action: Erase 4, 9 from R5C2; erase 2, 7 from R5C7. Both cells now show only {1, 6} — and you have effectively converted a Hidden Pair into a Naked Pair, which then cascades eliminations across Row 5 and any box they share.

Example 2: Hidden Pair in a 3x3 box

Hidden Pairs are most common in boxes that already have several digits placed. In the center box below, suppose 4, 9, 7, 8, 2 are already filled in. You check the remaining four empty cells and find:

• Digit 3 can only fit in two of the four empty cells.
• Digit 5 can only fit in the same two cells.
• The other two empty cells still have many candidates — the pair is buried.

Once you erase everything except 3 and 5 from those two cells, the other two empty cells in the box lose their 3 and 5 candidates too (those digits are now spoken for). Frequently this cracks the box completely.

How to spot Hidden Pairs

Scan by digit, not by cell. For each row, column, or box:

1. List the digits not yet placed in this unit.
2. For each missing digit, find the cells in the unit where it could go (using pencil marks or by elimination).
3. Look for two digits that share the exact same two cells.
4. Found a match? Erase every other candidate from those two cells.

Tip: in practice, the easiest place to start is a box that already has 5+ digits filled. With only 3–4 empty cells, the math is fast and Hidden Pairs surface quickly.

Common beginner mistakes

• Forgetting to scan by digit. If you only scan cells, you will miss every Hidden Pair. The technique requires a different mental gear.
• Confusing "the same two cells" with "overlapping cells". Digit X in {R1C2, R1C5} and digit Y in {R1C2, R1C7} share only one cell — not a Hidden Pair.
• Forgetting the cleanup. Finding the pair only matters if you also erase the other candidates from those two cells. The elimination is the whole point.
• Outdated pencil marks. Hidden Pairs depend on accurate candidates. Update your pencil marks after every solved cell — otherwise you will chase ghosts.

Hidden Pair extends to Hidden Triple and Hidden Quad

The same logic scales: if three digits can only fit in the same three cells (in any arrangement), you have a Hidden Triple — erase everything else from those three cells. Four digits in four cells gives a Hidden Quad. These are rarer but use the identical thought process.

Master Hidden Pairs first. Once your brain is comfortable scanning by digit, the larger variants are just "the same trick with one more layer".

Try it on a real puzzle

Hidden Pairs typically show up on Medium and Hard puzzles, after you have used Naked Singles, Hidden Singles, and Naked Pairs to make initial progress. Open a Medium puzzle on SudokuHint, fill in pencil marks once the obvious cells are placed, and start scanning by digit. The 💡 Hint button will surface Hidden Pairs when they appear — with the same thinking-path breakdown you have read here.

Article draft v1 · pending native-speaker review