Learning the hidden pair sudoku technique is a great way to start solving more complex sudoku puzzles. If you are getting stuck on intermediate or hard puzzles, this is a good strategy to use.
When to use the hidden pair technique?
This is a good technique to use when you have filled in all of the cells that you can using techniques such as singles. Hidden pairs helps you to start eliminating candidates which reduces the noise and allows you to easily spot other candidates.
What is a hidden pair?
A hidden pair is when a set of two numbers appear as candidates in only two cells within a specific “house” either 3x3 block, row, or column.
Since the cells can contain other candidates, this often hides the pair of candidates, which is why this technique is referred to as hidden pair.
This pair indicates that the cell only has two options since the numbers are unable to go anywhere else in the house.
How to spot a hidden pair
Let’s go over the steps to finding a hidden pair when solving a Sudoku puzzle.
- Start with a house that has many notes to focus on. Either a 3x3 block, row or column.
- Scan through each of the candidates until you find a candidate that is in exactly two cells within the house.
- Look in these two cells to see if there is another number that is only present in these two cells.
- You are now able to remove all other candidates from these two cells that are not the hidden pair.
Hidden pair example
Let’s go over an example and walk you through one step at a time to help understand how the hidden pair technique can be applied.
We will start by focusing on block seven which is highlighed in red on the Sudoku grid below.
Since we need notes to apply this technique, we will enter in all of the possible candidates in this 3x3 block.
We can now see the notes that have been added to the five empty cells that are highlighted in blue. We can start scanning these notes until we find a candidate that is only present in one other cell.
We can see that there is only a two in cells (c4, r9) and (c6, r9). Next we can look at both of these cells to try and find another number that is not present in the other cells of this house. We can see that the number eight is only present in both these cells.
This means that we have found a hidden pair (2,8) in cells (c4, r9) and (c6, r9). Since these cells have to be either a two or eight we can remove the four, six and nine from these two cells.
We can now see that the notes in cells (c4, r9) and (c6, r9) have been reduced to only two candidates. We are also able to remove more candidates based on this hidden pair. For simplicity the notes from the other 3x3 blocks have been removed, but we would be able to eliminte two and eight from any of the cells in r9 highlighed in blue below.
Often times the powerful eliminations that come from finding hidden pairs helps uncover singles that can be filled in or enables other more advanced techniques. When the other candidates in a hidden pair are eliminated the pair now becomes a naked pair.
Hidden pair vs. naked pair
Both a hidden pair and a naked pair are when two cells in a house are the only options for a cell. With a hidden pair the two cells that contain the pair also have other candidates mixed in amoung other candidates. In a naked pair the pair are the only candidates.
Finding these pairs is a good first step in solving sudoku puzzles using more difficult techniques.
Tips for applying the hidden pair technique
- Take more time when scanning the Sudoku grid. This strategy is more advanced than the hidden single technique.
- When looking for hidden pairs start with 3x3 blocks before moving onto rows and columns
Now that you know how to apply this strategy, test it out on one of our Sudoku puzzles!
Prerequisites
Before learning Hidden Pairs, you should be comfortable with:
- Candidate notation (pencil marks) — complete candidates in every cell
- Hidden singles — the simpler hidden subset technique
- Naked singles — the most fundamental technique
Common Mistakes to Avoid
Not checking all three house types. Hidden pairs can appear in rows, columns, AND boxes. Don’t only scan boxes.
Forgetting to remove other candidates. Once you find a hidden pair, remove ALL other candidates from those two cells — not just one.
Confusing with naked pairs. In a hidden pair, the two cells contain other candidates mixed in. In a naked pair, the cells contain only the two pair digits.
Incomplete pencil marks. Missing candidates can hide the pair or create false positives.
Looking for exact matches only. The two pair digits don’t need to be the only candidates — they just need to appear in only those two cells within the house.
When to Look for Hidden Pairs
Hidden Pairs are an intermediate technique — use them after exhausting:
- All naked singles and hidden singles
- Before or alongside naked pairs
Hidden Pairs appear regularly in Hard and above puzzles. They’re also useful in Medium puzzles that require more than just singles.
Frequently Asked Questions
What is the difference between a hidden pair and a naked pair?
In a naked pair, two cells contain ONLY the same two candidates. In a hidden pair, the two candidates appear only in those two cells within the house, but those cells also contain other candidates. The naked pair eliminates from OTHER cells; the hidden pair eliminates from ITS OWN cells.
Can a hidden pair become a naked pair?
Yes. When you remove the extra candidates from a hidden pair’s cells, the pair becomes a naked pair. This is the normal result of applying the hidden pair technique.
How common are hidden pairs?
Hidden pairs appear regularly in Hard, Expert, and Evil puzzles. They’re one of the core intermediate techniques every solver should know.
Should I look for hidden pairs or naked pairs first?
Look for whichever you spot first. Many solvers find naked pairs easier to see, but hidden pairs can sometimes be found more quickly by counting candidate occurrences per house.