Main Page - Back
 
Hidden Candidates
From sudokuwiki.com, the puzzle solver's site
breakline
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.
Hidden Pair Example


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.

Hidden Pair Example


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:

Hidden Pair Example


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.
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, we don't need exactly three pairs of numbers in three cells for the rules to apply. In the example below we have 4/8/9, 4/8 and 8/9 in three cells.

Hidden Triple Example


Since 4 AND 8 AND 9 must exist in those three squares the other numbers cannot exist there. So we remove them. This reveals the hidden triple:

Hidden Triple Example


The minimum number of numbers for Hidden Triples will be three pairs of numbers, for example, 4/8, 4/9 and 8/9. It is clear they are bonded together and if they lie on three cells within the same ROW, COLUMN or BOX then any other numbers on those cells can be removed.
Hidden Quads

Here is the one example of a Hidden Quad I found in a set of 18,000 sudoku puzzles. Four numbers 3/5/6/7 on four cells are hidden by all of one number - 4 in R2C8. 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 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 {1,6,7,8} and exists only in those four cells. Therefore other canidates (yellow/red text) can be removed 		Hidden Quad
Hidden Quad: Load Example or : From the Start

breakline

Comments...

Saturday 5-Jun-2010

... by: Lloyd Pape

Hi, I get confused. I have a row: 24,14,1245,257,2567,3,1267,8,9 ,..I would like to group cols 1,2 and 3 with a tripple, 24,14,124,delete the 5 in col 3,...then, delete the 2 incol4, the2 in col 5 and the 12 in col 7,..so that I end up with a tripple ,1,2,4, another tripple 5,6,7 and 3,8,9,...does this work,..if so , are the tripples naked or hidden,...thanks for your info to date,....regards,...lloyd

Thursday 6-May-2010

... by: Sarah

Hi Andrew,
Great site. I'm terrible at spotting hidden triples. Any tips, hints on becoming better at this?
Thanks!
Sarah

Monday 8-Mar-2010

... by: csvidyasagar

You have given an excellent example of Hidden Pairs, Hidden Triples and Hidden Quads. But the example you quoted of Mr Klaus Brenner of Hidden Quad, I suppose is NOT Correct. For hidden pairs, the digits must appear only in two cells like you correctly shown as 58 in your example. The digits 5, 8 do not appear in any other cell of the box. In Hidden Triples of digits 4, 8, 9 lie in only three cells and none of them appear in any other cell in the box. Similarly in Hidden Quads of your example, the digits 3,5,6,7 appear only in four cells in the Box and do not appear in any other cell of Column 8. But it is not so in the example cited of Mr Klaus Brenner. May be I am wrong or my understanindg of Hiddens is wrong. So can you explain how Hidden Quads are there in the example of which you have high lighted some cells.

Andrew Stuart writes:
The Hidden Quad is {1,6,7,8} and exists only in those four cells. Therefore other canidates (yellow/red text) can be removed.

Monday 15-Feb-2010

... by: robin smith

Hi, What a great site . it's so helpful when I really get stuck with a puzzle. One minor point . . would it not be possible to have the original numbers in the puzzle in a different colour so it is more easy to spot the ones that get added as the solution unfolds.

Just a thought.

But it's stil a great site.

Robin Smith

Andrew Stuart writes:
Orginal colours (clues) are red, solved cells are blue. There may be the odd diagram which I have snapped where this is not the case and i'll be replacing when I spot those

Tuesday 1-Sep-2009

... by: Chuck Bruno

Hello Andrew,

I have written several times but I must repeat "This is a great site". That being said, I have a question:

How do you determine what the difficulty level should be for a given stratagy?

I personally find that Pointing Pairs, Box/Line Reduction, X-Wing, and Unique Rectangles, are much easier to spot than Hidden Triples. When I get stumped on a Sudoku, I import it into your Solver, uncheck stratagies I don't usually look for, and step through it. In most cases, I find that I simply overlooked something silly. In some cases however, the Solver finds a hidden double or triple. Because these can't be turned off like the more difficult stratagies, I can't force the Solver around it to see if one of the other stratagies that I normally use, would allow the puzzle to be solved without using the naked double or triple.

In summary, I would like to be able to selectively turn off the "easier" stratagies just as can be done with the tougher ones.

Thanks for your time,

Chuck Bruno

Andrew Stuart writes:
Sorry for the late reply. All valid points, I might have a go at that - but trying not to over complicate an already complex interface.

Add your comments

A confirmation email will be sent to you after submitting.

Your Name

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

Your comment or question

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. If you want to be remembered, the check box above will store a cookie with your name and email address on your computer.

Line breaks and paragraphs are automatically converted — no need to use <p> or <br> tags.



Article created on 9-April-2008. Views: 67984
This page was last modified on 2-July-2009, at 05:05.
All text is copyright and for personal use only but may be reproduced with the permission of the author.
Copyright Andrew Stuart @ Scanraid Ltd, 2009