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V Hard 4 June - Now unique rectangles?

 
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George Woods



Joined: 28 Mar 2006
Posts: 231
Location: Dorset UK

PostPosted: Sun Jun 04, 2006 10:59 am    Post subject: V Hard 4 June - Now unique rectangles? Reply with quote

Very hard has now included X wings aa a technique that must be used to solve. But today's seems to use a Unique Rectangle- unless you know better.

The solution proceeds without even using a hidden pair, until a crunch point where 49 s in col1 r 7 and 9 and r9c6 denies either 4 or 9 in r7c6 and so on to the solution.

So is this use of unique rectangle a first, and is it the only way?
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Sun Jun 04, 2006 12:07 pm    Post subject: One way Reply with quote

You can solve it with an X-wing.

Keith
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sun Jun 04, 2006 12:24 pm    Post subject: Reply with quote

Multiple colouring/strong links on 6's also solves it.
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kkklau



Joined: 31 May 2006
Posts: 2

PostPosted: Sun Jun 04, 2006 1:55 pm    Post subject: Reply with quote

x wing of 6 at column 3 and 5
after that it's straight forward
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gigi



Joined: 04 Jun 2006
Posts: 5
Location: Central Texas

PostPosted: Sun Jun 04, 2006 7:39 pm    Post subject: Reply with quote

Howdy from Texas y'all... I'm so hooked on Sudoku! I've been visiting here from time to time to solve the puzzles and learn new techniques.

But in regard to today's puzzle (June 4 - VHard), I found that the X-Wing solution that kkk posted (solve off the 6 in Cols 3 and 5) didn't work for me. I thought I was losing my mind! Shocked Not sure where I went wrong.... (E-mail me kkk if you can figure out how I messed up)

But...

I did X-Wing off the 9's in Cols 1 and 6 and solved it with no problem.

I did a little more reading on X-Wing techniques just to confirm I wasn't going nuts... (still consider myself a novice for the most part)... and here is a good explanation how X-Wing works for anyone that is interested.... Unlike the 6's in kkk's post, I played off the 9's because there were no other options for the 9's in those rows as discussed in the following link!!

http://www.sadmansoftware.com/sudoku/technique6.htm

Have a great week!

gigi

[url][/url]
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Marty R.



Joined: 12 Feb 2006
Posts: 5061
Location: Rochester, NY, USA

PostPosted: Sun Jun 04, 2006 9:12 pm    Post subject: Reply with quote

After filling in the cells with their candidates and using basic techniques to eliminate candidates, I noticed in rows 36 and columns 89, a “Type 1” rectangle of 57-57-57-3567. Thus, the 57 gets eliminated from the fourth cell, leaving a 36. After more basic eliminations, I see another Type 1 rectangle in rows 79 and columns 16 of 49-49-49-1469. So the 49 is removed from the last cell, and that allows the puzzle to be completed with basic techniques.

In this thread, we have seen mention of X-Wings, Unique Rectangles, Multiple Coloring and Strong Links. It seems that I am writing every other day how it never ceases to fascinate me how many different approaches and techniques can be used to solve a given puzzle, and this one is certainly no exception.
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Sun Jun 04, 2006 10:17 pm    Post subject: Here is the grid Reply with quote

Here is the grid:
Code:

+----------------+----------------+----------------+
| 2    46   5    | 46   9    7    | 3    1    8    |
| 7    138  9    | 5    13   138  | 6    2    4    |
| 136a 48   16   | 2    136  48   | 9    57   57   |
+----------------+----------------+----------------+
| 36   5    4    | 1367 8    136  | 2    367  9    |
| 136  136  7    | 9    2    5    | 8    4    36   |
| 8    9    2    | 367  4    36   | 1    3567c 57  |
+----------------+----------------+----------------+
| 49   2    3    | 146  5    1469d| 7    8    16   |
| 5    16   8    | 136  7    2    | 4    9    136  |
| 49   7    16   | 8    136  49   | 5    36b  2    |
+----------------+----------------+----------------+

The X-wing is on <6> is in R39C35. It allows yout to eliminate <6> in the cells labeled "a,b".

The first UR (Type 1) on <57> is in R36C89. It allows you to eliminate <57> from "c".

The second UR (Type 1) on <49> is in R79C16. It allows you to eliminate <49> from "d".

Best wishes,

Keith
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George Woods



Joined: 28 Mar 2006
Posts: 231
Location: Dorset UK

PostPosted: Wed Jun 21, 2006 5:34 pm    Post subject: Another rewarding UR! Reply with quote

Keith
I was revisiting and looked at your "crunch point" with 1 x wing and 2 URs.Another UR you didn't mention is the 16 in r39 c35 The need for a 3 in this makes r2c5 1 and it solves so quickly after this one that it must be an A grade move!!!!
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Thu Jun 22, 2006 12:05 am    Post subject: Not really a "UR" Reply with quote

George Woods wrote:
Another UR you didn't mention is the 16 in r39 c35

Just a tecnical observation, George -- this isn't a "non-unique rectangle" because the corners lie in four separate 3x3 boxes. A true "UR" always has its four corners in two 3x3 boxes. dcb

PS It does happen to work out, but I think that's just a happy accident.
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