Hidden Pairs is a powerful intermediate technique that complements Naked Pairs by taking the opposite perspective on candidate subsets. While a Naked Pair involves two cells that contain only two candidates, a Hidden Pair involves two candidates that appear in only two cells within a unit, but those cells may contain additional candidates as well. The hidden nature comes from the fact that the pair is obscured by extra candidates in the same cells.
When two digits can only appear in the same two cells within a row, column, or box, those two digits must occupy those two cells. This means all other candidates in those two cells can be safely removed, effectively turning the Hidden Pair into a Naked Pair. For example, if digits 2 and 5 only appear as candidates in cells A and B of a row, then A and B must contain 2 and 5, regardless of whatever other candidates they might also show.
Hidden Pairs require you to examine candidate distributions from the digit's perspective rather than the cell's perspective. Instead of asking which cells have few candidates, you ask which digits appear in only a few cells. This shift in thinking is crucial for advancing your Sudoku skills and prepares you for Hidden Triples and other hidden subset techniques.
Try It Yourself
Walk through each step of the hidden pairs technique on a real puzzle. Follow the instructions and try entering the correct value when prompted.
Examine row 1 (index 0). Cells (0,4) and (0,5) are the only empty cells. List all the candidates for each cell by checking which digits 1-9 are missing from this row.
Step-by-Step Guide
Choose a row, column, or box to analyze and list all remaining candidates.
For each candidate digit, note which cells in the unit can contain that digit.
Look for two digits that appear as candidates in exactly the same two cells.
Confirm that no other cells in the unit can contain either of those two digits.
Remove all other candidates from those two cells, leaving only the hidden pair digits.
Check if the simplified cells trigger further eliminations or reveal singles.
Repeat the process for other units in the grid.
Imagine two rare books that only fit on two specific shelves. Even though those shelves hold other books too, you know the rare books must go there, so you can remove everything else from those shelves to make room.
Every digit must appear exactly once in a unit. If two digits have only two possible cells within that unit, those two cells are the only way to satisfy both placement requirements. Since two cells can hold at most two distinct digits, those cells are fully committed to the pair, and any other candidates in those cells represent impossible assignments that would leave one of the pair digits with no valid placement.
When to use: Use Hidden Pairs when scanning for Naked Pairs turns up nothing. Instead of looking at cells with few candidates, flip your perspective and ask which digits only appear in two cells within a unit.
Common Mistakes to Avoid
Only looking at cells with small candidate lists. Hidden Pairs often lurk in cells with many candidates, so cells with 4 or 5 candidates are easy to overlook.
Focus on digits rather than cells. Count how many cells each digit can go in within a unit. If two digits each appear in only two cells and those cells are the same, you have a Hidden Pair.
Forgetting to remove the extra candidates from the Hidden Pair cells after identifying the pair.
Once you confirm a Hidden Pair, strip every candidate except the two pair digits from both cells. This simplification is the whole point of the technique.
More Examples
See hidden pairs applied in different puzzle configurations to strengthen your pattern recognition.
Row Hidden Pair
Highlighted cells show the hidden pairs pattern
Practice Puzzles
Apply the hidden pairs technique on these mini challenges. Tap a highlighted cell and enter the correct digit.
Quick Reference
- Pattern:
- Two candidates appear in only two cells within a unit
- Action:
- Remove all other candidates from those two cells
- Look for:
- Two digits confined to the same two cells in a unit