Sudoku Hidden Pairs: A Worked Example

Hidden pairs reward patience. Two digits can only fit in the same two cells of a row, column, or box — even when both cells still look cluttered with other candidates. Once you spot the pair, you erase everything else from those two cells for free.

This guide is a worked example, in the same spirit as pointing pairs: exact cells, exact digits, exact eliminations. By the end you’ll be able to scan for hidden pairs on your own grid.

We use standard notation: r4c5 means row 4, column 5. Boxes are numbered left-to-right, top-to-bottom, so Box 1 is rows 1–3, columns 1–3.

The idea in one sentence

If two digits, within a single group, can only go in the same two cells — and nowhere else in that group — then those two cells belong to those two digits alone, so every other candidate in those two cells can be erased.

That’s the whole technique. The skill is scanning by digit instead of by cell.

Set up the example

Suppose you’re partway through a puzzle. Focus on Box 5 (r4c4–r6c6). Four cells are already filled (shown as plain digits); five are still empty, and you’ve pencilled their candidates:

Box 5 — pencil marks (filled givens shown as single digits)
          c4           c5           c6
 r4  [  2 6 9    |     3      |    4 5    ]
 r5  [   4 9     |   2 5 6    |     7     ]
 r6  [    1      |     8      |    5 9    ]

The five empty cells are r4c4, r4c6, r5c4, r5c5, r6c6. The five digits still missing from this box are 2, 4, 5, 6, 9.

Spot the hidden pair

Walk the missing digits and ask: in how many cells of this box can each one go?

• 2 → r4c4, r5c5 (two cells)
• 4 → r4c6, r5c4 (two cells)
• 5 → r4c6, r5c5, r6c6 (three cells)
• 6 → r4c4, r5c5 (two cells)
• 9 → r4c4, r5c4, r6c6 (three cells)

Two digits — 2 and 6 — land on exactly the same two cells: r4c4 and r5c5. Nowhere else in the box can either digit go. That’s a hidden pair.

Notice neither cell looks like a pair yet: r4c4 still carries a stray 9, and r5c5 still carries a stray 5. Scanning cell-by-cell for a naked pair (two cells that show only the same two candidates) would walk right past both of them. Scanning digit-by-digit is what reveals the pattern.

Make the deduction

The box must place a 2 and a 6 somewhere, and the only cells that can take them are r4c4 and r5c5. Between the two of them, those cells are entirely spoken for — one is 2, the other is 6 (we don’t yet know which is which). That means every other candidate sitting in r4c4 or r5c5 is impossible: it would need a cell to land in, and both available cells already belong to 2 and 6.

1. Erase 9 from r4c4, leaving {2, 6}.
2. Erase 5 from r5c5, leaving {2, 6}.

Nothing changes anywhere else in the box — the elimination lands entirely inside the pair itself.

Why the elimination matters

Eliminations inside a hidden pair rarely finish a puzzle by themselves, but they clear the clutter that hides the next move.

Suppose row 4 also carries a stray 9 pencilled at r4c8, and nowhere else in row 4 outside r4c4. Before the hidden pair, r4c4 still looked like a live option for row 4’s 9. Once the stray 9 is gone from r4c4, r4c8 is the only cell left in row 4 that can hold a 9 — a hidden single, ready to place.

The hidden pair itself never touched row 4. It just cleaned up two cells enough that a different group’s pattern became visible.

Hidden pairs on a row or column (the mirror case)

The same logic runs across rows and columns, not just boxes. Picture a different grid: Row 2 has four empty cells left — r2c1, r2c4, r2c7, r2c9 — and the row still needs 3, 5, 8, and 9.

Candidates: r2c1 = {3, 5, 9}, r2c4 = {8, 9}, r2c7 = {3, 5}, r2c9 = {8, 9}.

Digits 3 and 5 both land only in r2c1 and r2c7 — nowhere else in the row. That’s a hidden pair. Erase the stray 9 from r2c1, leaving {3, 5}; r2c7 was already clean.

Box, row, or column — it’s the same rule: two digits confined to the same two cells, wherever those cells sit.

How to scan for it efficiently

You don’t need to test every pair of digits in every group. Scan with intent:

1. After singles stall and pencilmarks are filled in, pick a group — row, column, or box — with several candidates left.
2. For each digit still missing from that group, list which cells can hold it.
3. Look for two digits whose cell-lists are identical and contain exactly two cells.
4. If you find one, strip every other candidate from those two cells and re-check for new singles.

Groups with four or five candidates left are the richest hunting ground — fewer live cells means digit-lists collide more often.

Hidden pairs vs. naked pairs

These two are the same fact, seen from opposite directions:

• Naked pair: two cells hold only the same two candidates and nothing else → erase those digits from the rest of the group.
• Hidden pair: two digits are confined to the same two cells, which may still hold other candidates too → erase everything else from those two cells.

Once fully reduced, a hidden pair and a naked pair describe the exact same two cells — they’re the same deduction, found by two different scans. The only difference is which one you can see first. If both cells in a pair still carry stray candidates, scanning by digit finds it before scanning by cell does — that’s the entire reason to learn hidden pairs as its own technique rather than waiting for naked pairs to appear on their own.

Practice it on a real grid

The fastest way to internalize hidden pairs is to hunt for one yourself. Puzzmint’s free browser beta is live now — play a Sudoku straight away, no download and no account. A fresh daily pair of logic puzzles lands at launch; for now the beta is open whenever you want to practise.

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For the bigger picture, see the complete how-to-solve-sudoku guide and the intermediate techniques roundup, which covers naked pairs, pointing pairs, and box-line reduction alongside hidden pairs. If pairs still feel unfamiliar, back up to naked and hidden singles first.

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