Hidden Pair
A Hidden Pair is two digits that can only go in the same two cells in a unit. Then the two cells must contain exactly these digits, and all other candidates in them can be removed.
Learn the techniqueNaked Pair
A Naked Pair is two cells in the same unit that have exactly the same two candidates. The two digits must share these cells between them, so they can be removed from the rest of the unit.
See the technique in practice
Work through the examples step by step. Each step explains what you see on the puzzle and why the conclusion holds.
Example:
- We write candidate notes in all the empty cells on the puzzle. Then we see which digits are still possible in each cell. Now we look more closely at column 2.
- Notice the two highlighted cells. Both have exactly the same two candidates, namely 1 and 5.
- The two digits must share these two cells between them. One cell gets 1 and the other gets 5. We do not yet know the order, but both cells are occupied either way.
- No other cells in column 2 can then contain 1 or 5. We remove the digits from the notes in row 9, column 2.
How to recognize the pattern
A Naked Pair is two cells in the same unit with exactly the same two candidates, no more and no fewer. With candidate notes on, you scan for two identical two-digit notes in the same row, column or box. The two digits must share the two cells, so no other cell in the unit can take them.
The pair itself does not directly solve any cells. The value lies in the eliminations: when the two digits disappear from the rest of the unit, new Singles or new Pairs often appear in the cells that lost candidates.
Step-by-step procedure
- Write candidate notes for all empty cells in the unit you are examining.
- Look for two cells that have exactly the same two candidates.
- Remove the two digits from all other cells in the same unit.
- Check whether the pair also shares another unit, because a pair in the same box and same row gives eliminations in both places.
- Look for new Singles in the cells that just lost candidates.
Common mistakes
- Accepting a cell with three candidates. Both cells must have exactly the two digits, or the logic does not hold.
- Removing from the wrong cells. The eliminations apply only to the unit the pair shares, not all neighbors of the two cells.
- Forgetting that the pair can lie in two units at once. Two cells in the same box can also share a row or column, and then the eliminations apply in both units.
When do you need the technique?
At Medium level it is no longer enough to place digits directly. Now it is about removing candidates: when you can prove that a digit cannot go in a cell, the rest of the puzzle becomes easier. Write candidate notes, because that is the key to all techniques from here on.
Try it on your own puzzle
Enter your puzzle in the Sudoku Solver and it will find the next step and explain the technique behind it.
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