Lesson:Hidden Pairs
If two candidates are only found in two specific cells within a unit...
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Hidden Pairs is an advanced candidate-elimination technique that becomes essential when simpler methods like Naked and Hidden Singles, and even Pointing Pairs, have been exhausted. A Hidden Pair exists when exactly two digits can only be placed in exactly two cells within a single unit (row, column, or box). Because those two cells are the only legal home for both digits, all other candidate digits in those two cells can be safely eliminated.
The word "hidden" reflects the fact that the pair of cells typically contains other candidates as well — making the pair harder to spot. The technique requires you to look at each digit's distribution across a unit and identify cases where two digits share only two cells as possible placements.
Hidden Pairs are particularly common in puzzles rated Hard and above. Learning to find them fluently gives you a powerful tool to crack open boards that seem completely stalled after simpler techniques have been applied. Once you eliminate the extra candidates from the Hidden Pair cells, a cascade of Naked Singles and Hidden Singles often follows.
How It Works — Step by Step
Step 1 — Build or review your candidate lists
Hidden Pairs require pencil-mark candidate tracking. For each empty cell, write down every digit that is still legally permitted by row, column, and box constraints. This step is essential — you cannot find Hidden Pairs by eye without knowing the full candidate sets.
Step 2 — Count positions per digit in each unit
For each unit, count how many cells each digit can legally occupy. Look specifically for digits that appear in only two cells within that unit. Make a note of which cells they land on.
Step 3 — Check for two digits sharing the same two cells
If you find two different digits that both appear in only two cells, and those two cells are identical for both digits, you have found a Hidden Pair. For example, digits 4 and 9 both only appear in Column C and Column F of Row 3 — that is a Hidden Pair.
Step 4 — Eliminate all other candidates from those two cells
Since those two cells must contain the Hidden Pair digits (in some order), every other candidate in those two cells is impossible. Remove all non-pair candidates from both cells. This often transforms each cell into a Naked Single or opens up Hidden Singles elsewhere.
When to Use This Technique
Reach for Hidden Pairs after you have applied Naked Singles, Hidden Singles, and Pointing Pairs and the board is still stuck. They are particularly productive on Hard-rated puzzles. If you see two digits each appearing in only two positions within the same unit, always check whether those positions overlap — a Hidden Pair is waiting.
Worked Examples
Consider a column where you have tracked all candidates. After placing several digits, you notice that the digit 2 can only go in Row 4 or Row 7 within that column. You also notice that digit 8 can only go in Row 4 or Row 7 of the same column. Both digits are confined to the same two cells. This is a Hidden Pair of {2, 8} in those two cells. Any other candidates those cells had — say, 1, 5, and 6 — can all be removed immediately.
In a 3×3 box, suppose five cells are filled. Of the four remaining cells, you find that digit 3 can only legally sit in the top-left or bottom-right cell of the box, and digit 7 can only legally sit in those exact same two cells. Remove all other candidates from those two cells. Often, this reveals that one cell now only holds a 3 and the other only holds a 7 — both become Naked Singles.
Frequently Asked Questions
How is a Hidden Pair different from a Naked Pair?
A Naked Pair is two cells that each contain exactly the same two candidates — you eliminate those two digits from the rest of the unit. A Hidden Pair is two digits that can only appear in two specific cells within a unit — you eliminate every other candidate from those two cells. They are mirror images of each other: Naked Pairs are spotted by looking at cells, Hidden Pairs by looking at digit distributions.
Do I need full pencil marks to find Hidden Pairs?
Yes. Hidden Pairs are impossible to find reliably without complete, up-to-date candidate lists for every empty cell. This is why the technique is considered intermediate-to-advanced — it requires disciplined pencil-mark tracking.
Can a Hidden Pair span different unit types?
A Hidden Pair is always defined within a single unit (one row, one column, or one box). However, after you apply the technique in one unit, the eliminations may cascade and create Hidden Pairs (or Naked Pairs) in overlapping units.
What comes after Hidden Pairs if the board is still stuck?
After Hidden Pairs, the next logical steps are Naked Triples, Hidden Triples, X-Wing, and Swordfish. Each of these techniques generalizes the pair logic to three or more cells/digits, or extends across multiple units using rectangular patterns.
Related Lessons
Ready to test your knowledge? Try applying this technique in our Hard Sudoku puzzles, Advanced Sudoku lessons or explore Expert Sudoku challenges. Keep training to improve your solve times and master the grid!
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