dailysudoku.com Forum Index dailysudoku.com
Discussion of Daily Sudoku puzzles
 
 FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

Unique rectangles

 
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Other puzzles
View previous topic :: View next topic  
Author Message
Marty R.



Joined: 12 Feb 2006
Posts: 5161
Location: Rochester, NY, USA

PostPosted: Mon Mar 06, 2006 2:58 am    Post subject: Unique rectangles Reply with quote

I am spotting unique rectangles from time to time, but, unfortunately, none have been the exact kind I've seen in examples and my logical reasoning skills, or lack of same, are a problem. I have one similar to the Unique Rectangle Type 3 from the brain bashers site, shown below, but I don't understand the explanation. (Only cols. 1Ė3 shown).

What does he mean by a locked set and a pseudo-single square? If there's a locked set of <18> in col. 1, why is he removing the "1" from r5c1 rather than the "1" or "8" from r9c1?



Code:
-------------
|789  6   79|
|5    2   1 |
|4    78  3 |
-------------
|3    9   2 |
|17   5   4 |
|6    17  8 |
-------------
|1789 4   79|
|2    37  5 |
|18   138 6 |
-------------


Unique Rectangles Type 3. There are almost two occurrences of a locked pair in <79>. However, we can never end up with all four squares only containing <79> otherwise we could swap the <7> & <9> and still have a valid solution, which is not allowed. Therefore, one of the values <1> or <8> must appear in one of R1C1 or R7C1, but we don't know which square, nor which number. But we can treat <18> as a pseudo-single square and look for a locked set containing it. We therefore have a locked set of <18> in C1 and can remove the <1> from R5C1. NOTE: the pseudo-single square can contain more than two additional numbers.
Back to top
View user's profile Send private message
Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Mon Mar 06, 2006 5:45 am    Post subject: Unique rectangles Reply with quote

Marty

I donít understand the terms or unique rectangles but, for what itís worth, the following comes to mind.

If you accept that 1 or 8 must be in r1c1 or r7c1, I think you can make the proposed elimination. If 1 occupies one of these cells it cannot enter r5c1. On the other hand if 8 occupies one of these cells, r9c1 contains 1 and again r5c1 cannot.

A locked set is a set with the same number of candidates as the order of the set. Here set means a subset of a column, a subset of a row or a subset of a box. You might have a set of two cells in one column which must contain 1 or 8. These values can then be eliminated from the other cells in the column.

In your fragment, either
- 1 is in r1c1 or r7c1 (when there is a locked pair (18) in r19c1 or r79c1 or
- 8 is in r1c1 or r7c1 (when there is a locked pair (18) in r19c1 or r79c1.
Whichever applies, 1 and 8 can be eliminated from all cells in column 1 except for r179c1. Here, of course, only the elimination of 1 is of any value.

Does this make any sense?

Steve
Back to top
View user's profile Send private message
keith



Joined: 19 Sep 2005
Posts: 3174
Location: near Detroit, Michigan, USA

PostPosted: Mon Mar 06, 2006 10:53 pm    Post subject: Unique rectangles Reply with quote

Marty,

It goes like this:


Explanation 1:

Code:


-------------
|789  6   79|
|5    2   1 |
|4    78  3 |
-------------
|3    9   2 |
|17   5   4 |
|6    17  8 |
-------------
|1789 4   79|
|2    37  5 |
|18   138 6 |
-------------



The unique rectangle has the two <79>'s as the floor, and the roof squares are <1789> and <789>. The rectangle cannot have <79> at all four corners, for then the puzzle will have no unique solution. So, at least ONE of the roof squares is not <7> OR <9>. ONE of them is possibly <7> OR <9>. The other possibilites in the roof squares are <1> and <8>.

Notice the bottom left square, it is <18>, and forms a triple ("Locked Set?) with the roof squares: <1, 8, 7 OR 9>. <7 OR 9> (the "Pseudo Single"?) is one possibility. So, no other squares in C1 can be <1>, R5C1 must be 7, etc.


Explanation 2:

Look at it another way: If R5C1 is <1>, then the first column of the puzzle reduces to


Code:


-------------
|79  6   79|
|5   2   1 |
|4   78  3 |
-------------
|3   9   2 |
|1   5   4 |
|6   17  8 |
-------------
|79  4   79|
|2   37  5 |
|8   138 6 |
-------------



which is not unique.


Explanation 3:

Maybe the following is clearer: At least one of the roof squares is not <7> OR <9>. However, <9> does not occur in any other squares in C1. So, one of the roof squares must be <9>, neither of them can be <7>, and R5C1 must be <7>.

The first explanation is a little more general; the third is, I think, easier to figure out.


Cute, isn't it?

Keith
Back to top
View user's profile Send private message
Marty R.



Joined: 12 Feb 2006
Posts: 5161
Location: Rochester, NY, USA

PostPosted: Tue Mar 07, 2006 1:36 am    Post subject: Reply with quote

Thanks Steve and Keith. I'd be lying if I said I could follow all that logic, but you both have given me some ideas as to approaches to these things that I wouldn't have otherwise realized. I'll try to apply them to the puzzle I'm working on, and if it doesn't work I'll be back.
Back to top
View user's profile Send private message
Display posts from previous:   
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Other puzzles All times are GMT
Page 1 of 1

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum


Powered by phpBB © 2001, 2005 phpBB Group