1Definition: Pairs consist of the same two candidate numbers in two cells of the same Lane or Block. Naked Pairs are Pairs where no other candidates appear in the two cells. Hidden Pairs are Pairs in which other candidates appear in one or both of the cells, but the two candidates of the matching pair do not appear elsewhere in the Lane or Block shared by the two cells.
Hidden Pairs (7,9) in yellow. Naked Pairs (5,6) in green.
3Look For: A cell with only two candidates, which matches another cell in the Lane or Block, with the same two candidates (Naked Pairs.) Or two candidates that only appear in two cells in the same Lane or Block (Hidden Pairs.)
4Consequence: For Naked Pairs: The two candidates can be erased from all other cells in the shared Lane or Block (or, if the Pairs share the same Lane and Block, then erase from the shared Block as well as from the shared Lane.) For Hidden Pairs Erase every other candidate from the Pairs' cells (in effect turning the Hidden Pair into a Naked Pair (which may allow for further erasures if the Pair shares the same Lane and Block.)
5Why it Works: For a Pair, there are two candidate numbers spread over two cells. So we know that one of the cells must be one of these candidates, and the other cell must be the other candidate. This leaves nowhere else in the shared Lane/Block for these two candidates to go. So, if these candidates appear in other cells of the shared Lane/Block, they can be erased, and if other candidates appear in the Pair's cells they can be erased.
7Note that this has changed the Hidden Pair into a Naked Pair. However, in this case that is irrelevant, as there are no other 7's or 9's in this row (if there were, it wouldn't have been a Hidden Pair to begin with.) It is only when a Hidden Pair's cells exist in the same Block that changing to a Naked Pair might result in further erasures (because there may be other instances of their candidates in the Block or shared Lane.)
8There is another Naked Pair on row 4 that is relevant: cells H4 and I4. The 5 and 6 are the only candidates for these cells. So, we know one of these cells must solve to a 5 and the other to a 6. Since these cells share row 4, we know that no other cell in row 4 can possibly be a 5 or a 6. We don't see any 6's in the row, but we do spot a 5 in E4, and so we erase 5 from E4.
9This causes a nice little chain-reaction of Naked Singles:
14Well done! This leaves several Naked Pairs on the board. Most are irrelevant, but the 5/6 in column I is not; it allows us to erase the 5 from I1 and the 6 from I3.
Notice how the 5/6 in I4 functions as half of the Pair for row 4, column I, and Block 6.
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