Solver App for Android and iPhone
Strategies for Number Puzzles of all kinds
Page Index
Solvers
Puzzles
Basic Strategies
Tough Strategies
Diabolical Strategies
Extreme Strategies
Depreciated Strategies
Str8ts
Other

Hidden Candidates

Hidden Pairs


Looking for Hidden Pairs is a great way to open up the board. This approach can remove a cluster of candidates from two cells and leave behind simple pairs which are the building blocks of more complex elimination strategies.


Hidden Pair example
Hidden Pair example : From the Start
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.
Three Hidden Pairs
Three Hidden Pairs : Load Example or : From the Start
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

Hidden Triples


We can extend Hidden Pairs to Hidden Triples or even Hidden Quads. A Triple will consist of three pairs of numbers lying in three cells in the same row, column or box, Such as [4,8,9], [4,8,9] and [4,8,9]. However, in just the same manner as Naked Triples we don't need exactly three pairs of numbers in three cells for the rules to apply. Only that in total there are three numbers remaining in three cells, so [4,8], [4,9] and [8,9] is equally valid. Hidden Triples will be disguised by other candidates on those cells so we have to prise them out by ensuing the Triple applies to at least on unit.

Two Hidden Triples
Two Hidden Triples : Load Example or : From the Start

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)
Hidden Quad
Hidden Quad : Load Example or : From the Start

Hidden Quads


Here is the one example of a Hidden Quad I found in a set of 18,000 Sudoku puzzles. Four numbers [3/4/5/7] on four cells are hidden by just two 6s in column 7. Barely qualifies as 'hidden' but it is legitimate. Note how none of the cells need to have all four numbers as long as only four cells contain all four numbers and are intermingled.

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.
Hidden Quad
Hidden Quad : Load Example or : From the Start

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.


Comments

Your Name/Handle

Email Address - required for confirmation (it will not be displayed here)

Your comment or question

Please enter the
letters you see:
arrow
Enter these letters Remember me


Please keep your comments relevant to this article.
Email addresses are never displayed, but they are required to confirm your comments. When you enter your name and email address, you'll be sent a link to confirm your comment. Line breaks and paragraphs are automatically converted - no need to use <p> or <br> tags.
Talk Subject Comments
Comments here pertain to corrections to the text, not the subject itself

Sunday 2-Feb-2014

... by: marten van der meer

Hidden quad example no 1. You are speaking about 3,5,6,7 in row B8, D8, E8, F8 but i can not find the number 3 in row B or in kolom 8.
Andrew Stuart writes:

Moved this to talk as I've since changed the Hidden Quad example 1

Sunday 2-Feb-2014

... by: marten van der meer

Hidden quad example. I can not find the number 3 in row B8 or in kolom 8
Andrew Stuart writes:

Moved this to talk as I've since changed the Hidden Quad example 1

Article created on 9-April-2008. Views: 249387
This page was last modified on 31-March-2012.
All text is copyright and for personal use only but may be reproduced with the permission of the author.
Copyright Andrew Stuart @ Syndicated Puzzles Inc, 2012