Lesson 8 of 10 · Pair technique
Hidden pairs: two digits with only two homes
The guide and all sudoku lessons
A naked pair starts with two squares that have only two candidates. For a hidden pair, start with two digits instead. If both digits can go only in the same two squares of one row, column or box, those squares must take them.
The squares may still show other marks. Those extra marks are what you can remove: the pair has already used both spaces. You do not yet know which of the two digits goes in which square.
Check the whole unit before erasing anything. Two digits appearing together is not enough if either digit has another possible home in that unit.
Example 1: In a box
Step 1 of 4
Read every candidate in the top-right box. Where can 1 and 3 go?
Look for 1 and 3 in the top-right box. Each has the same two possible homes: row 3, columns 8 and 9. The first square shows 1, 3 and 9; the second shows just 1 and 3.
Those two squares must hold the 1 and the 3 between them. Cross out the 9 at row 3, column 8. You have found a pair, not two placements: both squares still have two candidates.
Example 2: In a column
Step 1 of 4
Read column 5 for the 8 and the 9, rather than looking for two tidy sets of marks.
In column 5, the only places for either 8 or 9 are rows 3 and 8. The candidates in row 3 look busy, but the other squares in the column have neither digit.
Focus on row 8, column 5. Its marks are 6, 8 and 9. The 8 and 9 must use the pair's two squares, so the 6 can be removed here. The two squares do not need to touch or share a box.
Try it yourself
A new board, and the same idea. Get it wrong and the board tells you why.
In column 1, the 1 and 2 can only go in rows 2 and 4. Which candidate can you remove from the ringed square at row 4, column 1?
Pick one candidate to cross out in the ringed square, not a digit to place.
How to spot it faster
- Choose a digit with only two possible homes in a unit. Check whether another digit has exactly the same two homes.
- Read every square in that unit, including ones outside the highlighted pair. One extra home breaks the argument.
- After clearing the extra candidates, scan the crossing units again. The cleaner marks may help without producing a placement straight away.
Common mistakes
Looking only at the two squares
The restriction comes from the whole unit. If a 1 or a 2 can still go elsewhere in that unit, those digits do not own the two squares.
Removing the pair's own digits
Keep the two digits that have nowhere else to go. Remove other candidates from their two squares, not from the rest of the unit as you would for a naked pair.
Questions
Further reading
Try it
Try a hard 9×9 and check any digits with two possible homes in a unit. That board may call for pointing or a naked pair first; a random practice deal is not a guaranteed hidden-pair exercise.
Play solo on a hard 9×9