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## Hidden CandidatesFrom sudokuwiki.org, the puzzle solver's site |

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Looking at the top of this moderate puzzle we see that 6 and 7 have been found in the first two boxes. Along with the 6 and 7 in columns 7 this pins the placement of 6 and 7 in the third box to A8 and A9. It still appears there are a great number of other candidates in A8 and A9 which is true up to a point. However these extra candidates 'hide' the true values for these cells. We have deduced that 6 and 7 must go in A8 and A9 and therefore we can clear off all the alternatives. This doesn't mean we know which way round the 6 and 7 will go - but we can make 6 and 7 a Naked Pair in those cells and see where it leads us.

This is a more interesting and complex set of Hidden Pairs. Three occur simultaneously. In the blue rectangle [2,4] form a Pair on D3 and E3 clearing of 3, 5, 6 and 7. The red cells indicate two Hidden Pairs based on [3,7] which form a neat corner of three cells. [3,7] is unique to two cell in row E and in column 7. The yellow highlighted cells can be removed

We can extend

This tough puzzle has two Hidden Triples: the first, marked in red, is in row A. Cell A4 contains [2,5,6], A7 has [2,6] and cell A9 contains [2,5]. These three cells are the last remaining cells in row A which can contain 2, 5 and 6 so those numbers must go in those cells. Therefore we can remove the other candidates.

Now that we've removed those candidates from the red cells, we can see in column 9 that [4,7,8] is unique to cells B9, C9 and F9. By the same logic we can clear off other candidates in those cells.

(The solver will not choose the second example as Naked Triples get their first)

Here is the one example of a

Hidden Quads almost always only occur in rows, columns and boxes where there are no clues or solved cells, so you can be forgiven for skipping them outside those circumstances.

Klaus Brenner in Germany has found a number of excellent Hidden Quads, and I include one here to show they do exist.

The Hidden Quad is {1,4,6,9} in Box 5 and exists only in the four cells [D4,D6,F4,F6]. Therefore other candidates (yellow/red text) can be removed.

This very special puzzle also produces a perfectly formed Empty Rectangle later on.