Hidden Pairs
Two digits that can only go in the same two cells of a unit — remove all other candidates from those cells.
What is Hidden Pairs?
A Hidden Pair occurs when two digits appear as candidates in exactly two cells within a unit (row, column, or box), and those same two cells are the only cells in the unit where both digits can appear. The pair is "hidden" because the two cells may have several other candidates — the matching pattern is not immediately visible from the cells' candidate lists, but from the perspective of the two specific digits. The key insight is this: since both digits are confined to just two cells, each of those two cells must contain one of the two digits. Therefore, all other candidates in those two cells are impossible and can be eliminated. A Hidden Pair effectively converts the two cells into a Naked Pair — once you remove the extraneous candidates, the pair becomes visible. This makes Hidden Pairs both an elimination technique and a pattern-revealing technique, as uncovering a Hidden Pair often exposes Naked Pairs, Pointing Pairs, or Singles that were previously concealed behind the extra candidates.
When to Use Hidden Pairs
Use Hidden Pairs after Pointing Pairs, Naked Pairs, and Box-Line Reduction when you need further candidate reductions. They often appear when the board has been partially solved and simple techniques no longer yield direct placements. To find them, instead of looking at cells and their candidates (as you do for Naked Pairs), reverse your perspective: look at individual digits and track which cells within each unit contain that digit as a candidate. When two digits each appear in exactly the same two cells of a unit (and only those two cells), you've found a Hidden Pair. This dual-perspective — "cell-centric" vs. "digit-centric" — is a hallmark of advanced Sudoku solving and greatly expands your pattern recognition capabilities.
How to Apply Hidden Pairs — Step by Step
- 1
Analyze each unit digit by digit
For a target row, column, or box, go through each digit from 1–9. For each digit, list all cells within the unit where that digit appears as a candidate. You're looking at the unit from the digit's perspective rather than the cell's perspective. This is the reverse of how you search for Naked Pairs.
- 2
Find digits appearing in exactly two cells
From your analysis, identify any digit that appears as a candidate in exactly two cells within the unit. Note these digits and their cell pairs. If a digit appears in only one cell, it's a Hidden Single (place it first!). If it appears in three or more cells, it cannot form a Hidden Pair by itself.
- 3
Check for two digits sharing the same cell pair
Compare the cell pairs of all digits that appear in exactly two cells. If two different digits share the exact same pair of cells — meaning digit A appears only in cells X and Y, and digit B also appears only in cells X and Y — you have found a Hidden Pair. Both digits are locked into those two cells.
- 4
Remove all other candidates from those cells
Now eliminate all candidates other than the two paired digits from cells X and Y. For example, if the Hidden Pair is {3, 7} in cells X and Y, remove every other candidate (1, 2, 4, 5, 6, 8, 9) from both cells. After this elimination, the cells effectively become a Naked Pair [3, 7], which may enable further eliminations in the unit.
💡 Pro Tip
Hidden Pairs are the "reverse" of Naked Pairs. Instead of looking at what candidates are in the cells, look at where each candidate can go in the unit. A practical technique: create a small frequency table for the unit. Write each digit 1–9 and next to each, list which cells in the unit contain that digit. Any two digits appearing in the same two cells form a Hidden Pair. Solvers who master both the Naked and Hidden perspective simultaneously can spot pairs — in both forms — significantly faster, because the two searches complement each other and cover all pair-type patterns in a unit.
Practice Hidden Pairs Now
Put this technique to the test on a live puzzle. The Practice Mode lets you work through real examples with candidate marking.