Hidden Pairs in Sudoku: A Complete Explanation
A hidden pair in Sudoku is when two digits appear as candidates in exactly two cells within a single row, column, or 3x3 box, and nowhere else in that unit. Spotting a [Hidden Pair](/techniques/hidden-pairs) lets you remove every other candidate from those two cells, simplifying the puzzle. While often missed by beginners, this technique is a powerful stepping stone between basic single-digit strategies and more advanced logic. This article answers the most common questions about finding and using hidden pairs.
What exactly is a hidden pair?
A hidden pair consists of two specific digits (like 3 and 7) that can only be placed in two specific cells within a single unit (a row, column, or 3x3 box). While those two cells may contain other candidate digits as well, the key is that the pair of digits do not appear as candidates in any other cell of that unit. Finding this pattern reveals that those two digits must occupy those two cells, which in turn means all other candidates in those two cells can be safely erased.
How do I find a hidden pair?
To spot a hidden pair, you must work with pencil marks, the small candidate numbers you note in empty cells. Scan each unit (row, column, box) individually. For every possible digit (1-9), check where it can go in that unit. You are looking for a pair of digits that share the same two possible cell locations within the unit and only those two locations. For example, if within a row, the digit 4 can only go in cells A and B, and the digit 8 can also only go in cells A and B, then 4 and 8 form a hidden pair in cells A and B.
- Focus on one unit at a time. Don't try to scan the whole grid at once.
- Look for digits that have very few possible placements (two or three) within a unit first.
Why does finding a hidden pair let me eliminate other candidates?
The logic is based on the fundamental rule of Sudoku: each digit must appear exactly once in every unit. If the two digits of the hidden pair can only be placed in those two specific cells, then those two cells are reserved for that pair. Therefore, no other digit can be placed in those cells. All other candidate numbers you may have penciled into those two cells become impossible and can be removed. This cleanup often reveals new Naked Singles or other patterns.
What's the difference between a hidden pair and a naked pair?
These are complementary techniques that work in opposite directions. A Naked Pair is when two cells in a unit contain only the same two candidates (e.g., just 2 and 5). You eliminate those two digits from all other cells in the unit. A hidden pair, however, starts with the digits: two digits are confined to two cells, but those cells are 'cluttered' with extra candidates. You eliminate the clutter *from the pair cells themselves*. In essence, a naked pair is obvious in the cells; a hidden pair is discovered by analyzing the unit.
Common mistakes and misconceptions
A frequent error is confusing a hidden pair with two cells that simply share some candidates. The defining condition is that the two digits must appear *only* in those two cells within the unit. If either digit can also go in a third cell, it's not a hidden pair. Another mistake is thinking the two cells must be adjacent or in the same box. For a row or column unit, the two cells can be anywhere in that line. Also, don't assume you only look for pairs in empty units; hidden pairs often appear in units that are partially filled.
Practice tips for mastering hidden pairs
Start by practicing on easier puzzles where you're forced to use pencil marks. Use our hint engine to identify when a hidden pair is available. When you find one, trace the logic: 'Digit A can only go here or here. Digit B can also only go here or here. Therefore, these two cells must be A and B.' This reinforces the pattern recognition. After finding a hidden pair, also look for a related pattern called a Pointing Pair, which can create the conditions for a hidden pair to form.
- Be systematic in your scanning. Go digit-by-digit (1 through 9) within a chosen unit.
- After eliminating candidates from a hidden pair, re-scan the affected cells and unit for new singles or pairs.
Key Facts
- ▪A hidden pair is two digits that can only be placed in two specific cells within a single row, column, or 3x3 box.
- ▪Finding a hidden pair lets you remove all other candidate numbers from those two cells, leaving only the pair.
- ▪Hidden pairs require full pencil marking to be visible; you cannot spot them by looking at given numbers alone.
- ▪The logic works because if two digits must occupy two cells, no other digit can go in those cells.
- ▪A hidden pair is different from a naked pair, where two cells contain only the same two candidates.
- ▪For a row or column hidden pair, the two cells can be in different 3x3 boxes as long as they are in the same row or column.
- ▪Spotting a hidden pair often reveals a subsequent naked pair in the same two cells after cleanup.
- ▪Mastering hidden pairs is a critical step before learning more complex strategies like X-Wing or Swordfish.
Frequently Asked Questions
Can a hidden pair be in two different 3x3 boxes?
Yes, if the hidden pair is in a row or column, the two cells may belong to different 3x3 boxes; they just must share the same row or column. If the unit is a box, both cells are in that same box.
Do the two cells of a hidden pair have to be empty?
No, but they must be unsolved. They will contain pencil marks (candidates). The hidden pair pattern is found among those candidate numbers.
What happens after I eliminate the extra candidates from a hidden pair?
The two cells become a naked pair containing only the two hidden digits. This may let you eliminate those two digits from other cells in the same row, column, and box.
How is a hidden triple different?
A hidden triple involves three digits confined to three cells in a unit. The same logic applies: you can remove all other candidates from those three cells, leaving only the triple.
Are hidden pairs only found in hard puzzles?
They are common in medium-difficulty puzzles and essential for hard ones. Easy puzzles can often be solved with just singles and naked pairs.