Hidden pairs
The mirror image of a naked pair, and considerably harder to see — because you are looking for an absence somewhere else rather than a pattern sitting in front of you.
The idea
If two digits can each only go in the same two squares of a unit, then those two squares must hold those two digits between them. Everything else in those two squares can be erased.
Compare the two directions and the difference becomes clear. A naked pair cleans up the rest of the unit. A hidden pair cleans up the pair itself.
A worked example
Look at the top-middle box, and follow the 2 and the 7.
Across the whole box, 2 and 7 appear as candidates only in r1c4 and r1c5. Those two squares must therefore take the 2 and the 7 in some order — so the 1 and the 4 come out of r1c4, and the 5 comes out of r1c5.
Notice the shape of the argument. Nothing about r1c4 on its own suggested this; it looked like an ordinary four-candidate square. The evidence was the absence of 2 and 7 everywhere else in the box.
How to spot them
Count digits, not squares. Go through a unit asking how many squares each missing digit could occupy, and write the count down if you need to. Two digits that both answer "these same two squares" are a hidden pair.
It follows that hidden pairs are easiest to find in the unit with the fewest empty squares, because there are fewer places for the counts to be large. When a puzzle stalls, start with the most complete box.
Common mistakes
The most frequent is finding one and then erasing the wrong things — clearing the two digits from the rest of the unit, as if it were a naked pair. That is not licensed, and it will usually break the puzzle. A hidden pair only tells you about the two squares themselves.
The second is missing them entirely because the squares look crowded. A hidden pair often hides inside squares showing five or six candidates, which is exactly where the eye does not want to go.
Common questions
What is a hidden pair in Sudoku?
Two digits that can only go in the same two squares of a unit. Those two squares have to take those two digits between them, so every other candidate sitting in those two squares can be erased.
How is a hidden pair different from a naked pair?
A naked pair is two squares showing only two candidates, and it clears those digits out of the rest of the unit. A hidden pair is two digits confined to two squares, and it clears the other digits out of those two squares. A naked pair prunes outward; a hidden pair prunes inward.
What do I erase when I find a hidden pair?
Everything except the two digits, and only inside the two squares. Nothing outside them changes. Once you have done it the hidden pair has turned into a naked pair, which may then let you eliminate outward as well.
Why are hidden pairs so hard to spot?
Because the two squares can each be carrying four or five candidates, so nothing about them looks constrained. You find them by counting where each digit can go in the unit, not by reading candidate lists and waiting for something short to catch your eye.
Where to go next
The next technique in the order is pointing pairs — A digit cornered onto one line inside a box clears that line in the two neighbouring boxes.
Coming to this cold? The step before it is naked pairs, and this technique is usually the one you reach for when that stops opening squares.
All nine techniques: the techniques index. New to the rules? Start here. Ready to use it? Open a board. Run a puzzle site? Embed this board.
Last reviewed