Hidden Pair Walkthrough
A Hidden Pair is two digits that appear in only the same two cells of a unit. Those cells must hold those two digits, so all other candidates can be stripped from them.
Below are 3 positions from real puzzles, each captured when the solver first needs this move. Find the pattern on each before-board yourself, then read the notes and check the after-board, where removed candidates are struck out in red and solved cells shown in green.
Example 1: There is a Hidden Pair in Row 5
In row 5 the digits 1 and 8 each have exactly two possible cells, and they are the same two: r5c6 and r5c8. r5c6 already shows nothing else, so the visible work happens in r5c8, which sheds 3 and 4 and goes from {1,3,4,8} to {1,8}. Half-hidden pairs like this are common. One cell of the pair is already clean, and you only notice the pattern by asking where the 1 and the 8 can go rather than what each cell holds.
Example 2: There is a Hidden Pair in Row 5
The pair r5c2 and r5c3 is hidden in two units at once: 1 and 8 are confined to those two cells within row 5 and also within box 4. Neither cell gives it away, since r5c2 lists five candidates and r5c3 three. Once 3, 4 and 5 come out of r5c2 and 3 comes out of r5c3, both read {1,8}. A tally of row 5 finds the pair, and so does a tally of box 4, which is a useful check that you have counted correctly.
Example 3: There is a Hidden Pair in Column 9
Down column 9, the digits 3 and 4 appear only in r7c9 and r8c9. Each of those cells carries one extra candidate, a 6 in the first and an 8 in the second, and the Hidden Pair removes both, leaving two {3,4} cells. The two cells are in box 9 as well, and 3 and 4 appear nowhere else in that box either, so the same pair is hidden in two units. Below them, r9c9 is {6,8}, the two digits the pair just shed.
Why the deduction is valid
A Hidden Pair is the mirror image of a Naked Pair. Rather than two cells confined to two digits, it is two digits confined to two cells: somewhere in this unit, digit A appears as a candidate in only these two cells, and so does digit B. Since both digits must be placed in the unit and both have only that pair of homes, they take one each. That means every other candidate in those two cells is impossible and can be deleted — the pair is revealed by stripping the clutter away.
How to spot a Hidden Pair on your own board
- Count candidate occurrences per digit within a unit rather than reading cells. Any digit appearing in exactly two cells of the unit is a lead.
- Two such digits sharing the same two cells is the pattern. Tallying the nine digits across one unit takes a few seconds and finds every Hidden Pair in it.
- Boxes tend to hide them best, because a box’s candidates are not laid out in a line where the eye naturally compares them.
Common mistakes
- Deleting the pair digits from the other cells of the unit. That is the Naked Pair action. Here the deletion happens inside the two cells, to everything that is not A or B.
- Giving up because both cells look busy. A Hidden Pair frequently sits in cells showing four or five candidates each — the clutter is what hides it.
What to do next
Once stripped, the two cells now form a Naked Pair, which may license further eliminations in any other unit the two cells share. Check whether they also sit together in a box or line.