Basic-Hidden Pairs

Hidden Pairs
Looking for Hidden pairs is a great way to open the board up to the other tests. Consider this top centre box below. There are two 5/8s hidden in in the squares at the top of the 3 x 3 box. They are marked by the green squares. We know these are the only possible positions for 5 and 8 since the rest of the board excludes the other squares in the box.

Since 5 AND 8 must exist in those two squares the two 1s, the 7 and the 9 cannot exist there. So we remove them. This reveals the hidden pair.

The knock on effect of this is to leave just one 7 in the box. We can make that the solution of that square and probably complete the rest of the board:

Exposing the pairs like this is essential for the Box/Line Reduction and the Remote Pairs - or at least makes them identifiable as appropriate strategies.

Basic-Naked Quads

Naked Quads
A Naked Quad is rarer, especially in its full form but still useful if they can be spotted. The same logic from Naked Triples applies.

We have a Naked Quad arranged nicely together in the top row. Because we have 2/4/7/8 in columns 3, 4, 5 and 6 (marked in green circles) we can clear all other occurrences from the row (marked in red squares).

Basic-Naked Triples

Naked Triples
A Naked Triple is slightly more complicated because it does not always imply three numbers each in three cells.Any group of three cells in the same unit that contain IN TOTAL three candidates is a Naked Triple. Each cell can have two or three numbers, as long as in combination all three cells have only three numbers. When this happens, the three candidates can be removed from all other cells in the same unit.

The combinations of candidates for a Naked Triple will be one of the following: The last case is interesting and the advanced strategy XY-Wings uses this formation. (123) (123) (123) (123) (123) (12) (123) (12) (23) (12) (23) (13)

To see a Naked Triple in action look at this center strip from an example board:



We have a triple in columns 1, 8 and 9. There are three other squares with 5,7 and 8 so we can clear them off leaving: