Hidden Pairs
How many cells contain each digit?
Hidden Pairs is the complement to Obvious Pairs, and considerably harder to spot. Where an obvious pair shows you two cells that list only two candidates each, a hidden pair shows you two digits that appear as candidates in exactly two cells within a region — a row, column, or 3×3 box — even though both of those cells list several other, unrelated candidates that hide the pattern.
Because Sudoku requires each of those two digits to appear somewhere in the region, and each has only two legal cells left, both digits must occupy those same two cells between them. Every other candidate sharing those two cells — digits that have nothing to do with the pair — can therefore be eliminated, even though it doesn't tell you which cell gets which digit. Hidden pairs appear often even on the hardest boards, and clearing their surrounding clutter frequently exposes an obvious single or hidden single underneath.
How It Works
A hidden pair is the complement of an obvious pair. Where an obvious pair shows you two cells each containing only two digits, a hidden pair shows you two digits that appear as candidates in exactly two cells within a region — hiding among others.
- Choose a region (row, column, or box).
- Find two digits that appear as candidates in exactly two cells within that region.
- If both digits appear in the same two cells — and nowhere else in the region — those two cells must hold those two digits.
- All other candidates in those two cells can be safely eliminated.
The pair itself cannot be resolved to specific cells yet. But the elimination it enables clears the way for other techniques.
Example
Below board presents an example of a hidden pair on digits 4 and 7, tucked inside a box alongside other candidates.
Digits 4 and 7 look unremarkable here — both cells have other candidates too. But scan the whole box for 4: it only appears in these two cells. Same for 7. That means 4 and 7 must occupy these two cells between them, whatever else their notes claim. The 1, 3, and 9 sharing those cells can be eliminated.
On Evil Boards
Hidden pairs are encountered very often on even the most evil boards. Applying the technique often results in creating naked singles or hidden singles. Experienced solvers check for hidden pairs while also checking for their sibling patters — obvious pairs and pointing pairs — at the same time.