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OK I've got a tuff one

 
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sideli123



Joined: 20 Dec 2005
Posts: 7
PostPosted: Sat Feb 04, 2006 4:41 pm    Post subject: OK I've got a tuff one Reply with quote
I've been solving evil and very hard puzzles now for months and havent been stumped. I find the doubles and triples but this puzzle has me scratching my head. Can someone help. It starts with this

--- -1- -48
9-- --- 2--
-53 7-- ---

--- --5 96-
3-- -9- --1
-89 4-- ---

--- --6 85-
--2 --- --6
54- -7- ---


I got it to this and can go no further

--7 -1- -48
918 --- 2--
453 7-- 619

--4 --5 96-
3-5 -9- 481
-89 4-- ---

7-1 --6 854
8-2 --- --6
546 -7- ---

Thanks for the help
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sat Feb 04, 2006 7:18 pm    Post subject: A route to the solution Reply with quote
There is a pair <26> in R1.

There is a triple <238> in C5.

There is a pair <45> in C5.

One you recognize these, then R6C5 is <6>, R2C4 is <6>, and the rest involves only pinned squares.

I hope this helps.

Keith
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
PostPosted: Sat Feb 04, 2006 7:29 pm    Post subject: This puzzle has two solutions Reply with quote
Hi, sidelit23! It's nice to hear from you.

You can break through the logjam at this position (below) by using a "double-implication chain." I've only shown the candidate lists that matter for the sake of this argument.
Code:
-   -   7    -   1   -    -   4   8
9   1   8    -   -   -    2   -   -
4   5   3    7  28  28    6   1   9

-   -   4    -   -   5    9   6   -
3   -   5   26   9   -    4   8   1
-   8   9    4  236  -    -   -   -

7  39   1   239 23   6    8   5   4
8   -   2    -   -   -    -   -   6
5   4   6    -   7   -    -   -   -

Let's examine what happens if we set r3c5 = 2. Then

A. r3c5 = 2 ==> r7c5 = 3 ==> r7c2 = 9
B. (r3c5 = 2 & r7c5 = 3) ==> r6c5 = 6 ==> r5c4 = 2 ==> r7c4 = 9

So r3c5 cannot be a "2", and it must be an "8". This value is enough to let you (almost) complete the puzzle. dcb

PS When I got close to the end of this one I ended up with a "swordfish" pattern that could be completed in two different ways. So I think this puzzle has multiple solutions. Oh -- I went back and checked more closely, and I found 6 distinct solutions. You can either find a "swordfish" with {3, 9} pairs or, by making a different choice, you can wind up with two independent "non-unique rectangles", one in {3, 9} and the other in {5, 7}.
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
PostPosted: Sat Feb 04, 2006 7:54 pm    Post subject: The "uniquity" assumption Reply with quote
Keith wrote:
Once you recognize these, then R6C5 is <6>, R2C4 is <6>, and the rest involves only pinned squares. ...

Hi, Keith!

We've had a discussion before about the "non-unique rectangles," and how one can sometimes solve a puzzle by recognizing them, or the closely related "BUG" pattern.

This puzzle is a pretty good example of the logical flaw in those methods. If you continue working through this you'll find a "non-unique rectangle" in r2c7, r2c9, r6c7, & r6c9. And if you make the assumption that the solution is unique you'll obtain a "3" at r2c7.

The only thing is, the solution you'll arrive at when you do this is not unique, because there are six cells in which "3" and "9" are interchangeable.

On top of that, if you assume that r2c7 <> 3 you'll arrive at a different set of solutions, with two embedded "non-unique rectangles."

Just thought you might be interested -- this is an edifying example. dcb
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
PostPosted: Sat Feb 04, 2006 8:53 pm    Post subject: Oops -- I miscopied the puzzle Reply with quote
Oops!

I just realized that I made a mistake when I copied this puzzle -- I inadvertently put the "2" that should be in r2c7 in r2c8 instead. That's why I found multiple solutions.

I still think it (this puzzle with the "2" misplaced) is an interesting example. dcb
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