A hidden pair is a subset of two candidates that appear only twice within a house and in exactly the same two cells. These two numbers can logically only go in one of those two cells and they can't go anywhere else in the house and all other candidates within those two cells can be eliminated. We just don't know which way round those two numbers will go yet.
In this grid, in row 1, there are two cells, A1 and E1 which are the only possible places for the numbers 2 and 8 within that row. '2' must be in A1 or E1, and '8' must be in A1 or E1. If A1 is '2' then E1 must be '8' and the opposite is true, if A1 is '8', then E1 must be '2'. There is simply nothing else that can go in either of those two cells and this means anything other than 2 or 8 can be eliminated.
That means 4, 5 & 6 can be elimnated from A1, and 4, 5, & 6 and be elimated from E1. This leaves us with the hidden single in I1, the last remaining cell in row 1 where '6' can appear.
In row/column notation this can be written as: 2,8 in r1c15 => r1c15<>4, r1c15<>5, r1c15<>6; r1c9=6.
By looking for the occurrence of two candidates that appear together in just two cells within a house, in this case a column, hidden among other candidates, we know that those two cells are limited to those two numbers and we can eliminate everything else from those two cells.
Here, the numbers 3 & 6 only appear in cells H5 and H9 within column 8 and each cell must be one of those numbers. We can eliminate 2 & 9 from H5 and 4 & 5 from H9. This leaves H7 as the last remaining possibility for '5' in column 8.
This hidden pair can be written as: 3,6 in r59c8 => r5c8<>2,r5c8<>9,r9c8<>4,r9c8<>5; r7c8=5
Sometimes more than one hidden single might be revealed and it won't necessarily be in the same house as the hidden pair, so don't stop looking because you've found one hidden single. The elimination of the candidates from H5 reveal a hidden single in the row 5 house, can you spot it?
The previous methods have looked at the intersection of a row or column with a box, but hidden pairs operate within a single house, which means you can find them in boxes too.
The numbers 2 & 9 are candidates in only A7 and C9 within box 7, meaning we can eliminate 7 from A7 and 3, 4 & 5 from C9, leaving C8 as the only position that '3' can go within box 7.
Hidden Pair: 2,9 in r7c1,r9c3 => r7c1<>7, r9c3<>3, r9c3<>4, r9c3<>5; r8c3=3
Again, a second hidden single has been revealed, this time in row 7 by the elimination in A7. The hidden pair in box 7 also affects r79c13. You will often find that the hidden single is revealed in two or three houses simultaneously, in this case the '3' in C8 is revealed as a hidden single in both box 7 and column 3.
Remember though, sometimes a hidden single might only reveal itself in a house different to which you found the hidden pair, so don't focus solely on that one house, look at the intersecting houses too.
Direct Claiming | Direct Hidden Triple
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