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Could be relatively easy ...

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keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Fri Dec 12, 2008 2:22 am Post subject: Could be relatively easy ...

Code:

Puzzle: BB55922sh
+-------+-------+-------+
| . . 3 | . . . | 4 . . |
| . 9 2 | 8 . 7 | 3 5 . |
| 7 5 . | . . . | . 2 8 |
+-------+-------+-------+
| . 1 . | . 2 . | . 9 . |
| . . . | 3 . 1 | . . . |
| . 4 . | . 7 . | . 3 . |
+-------+-------+-------+
| 6 3 . | . . . | . 4 9 |
| . 8 4 | 5 . 6 | 2 7 . |
| . . 9 | . . . | 8 . . |
+-------+-------+-------+

Keith

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Fri Dec 12, 2008 3:21 am Post subject:

Code:

.------------------.------------------.------------------.
| 8 6 3 | 2 5 9 | 4 1 7 |
| 4 9 2 | 8 1 7 | 3 5 6 |
| 7 5 1 | 46 346 34 | 9 2 8 |
:------------------+------------------+------------------:
| 3 1 5678 | 46 2 58 | 567 9 45 |
| 9 27 567 | 3 46 1 | 567 8 245 |
| 25 4 568 | 9 7 58 | 156 3 125 |
:------------------+------------------+------------------:
| 6 3 57 | 17 8 2 | 15 4 9 |
| 1 8 4 | 5 9 6 | 2 7 3 |
| 25 27 9 | 17 34 34 | 8 6 15 |
'------------------'------------------'------------------'

Quote:

one stepper
mixed ending w-wing, {2,5}r6c1 and {1,5}r7c7 connected via the strong links on 5 in row 9... extend via the 1's...
(2=5)r6c1 - (5)r9c1 = (5)r9c9 - (5=1)r7c7 - (1)r6c7 = (1)r6c9; r6c9 <>2
or with the contradiction/victims...
(2)r6c9 - (2=5)r6c1 - (5)r9c1 = (5)r9c9 - (5=1)r7c7 - (1)r6c7 = (1-2)r6c9; r6c9 <> 2

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Fri Dec 12, 2008 5:02 am Post subject:

A couple of UR's, an XY-wing, and a BUG+1 to finish up. One of those rare puzzles where the uniqueness journey is quite pleasant. May I also ask: What is the point of these really complicated "one-stepper" solutions? Get off the freeway! Take the side roads! It's the journey, not the destination. Keith

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Fri Dec 12, 2008 9:35 am Post subject:

Quote:

May I also ask: What is the point of these really complicated "one-stepper" solutions?

Keith,
trust me. finding that chain was a journey. it was a cart path over that puddle that no one walks through...

yeah...

while fending off swarms of bees, escaping my neighbors rabid dog, while my boss is yelling in my ear, and I can't catch a breath fumbling through my keys to my car... all before falling contently on my bed.

yep, it was a journey. hope you can see that better now. sorry it wasn't evident before. Smile

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Fri Dec 12, 2008 2:33 pm Post subject:

Norm, I apologize, I was not meaning to pick on you. Keith

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Fri Dec 12, 2008 10:41 pm Post subject:

storm_norm wrote:

Code:

Quote:

Norm, I don't want you to go to a lot of trouble, but could you explain without the notation? I can see that, because of the SL on 5 in r9, that r6c1 must=2 or r7c7 must=1. Then testing for each reveals that r6c9 can't be=2. However, what I did there is a forcing chain which was pointed to by the strong link. Is there a more sophisticated reasoning to determine the result?

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Fri Dec 12, 2008 11:21 pm Post subject:

Norm wrote:

mixed ending w-wing Question

What I see is an ordinary discontinuous loop that doesn't need cells [r7c7] and [r6c7].

Code:

(2=5)r6c1 - (5)r9c1 = (5-1)r9c9 = (1-2)r6c9 = (2)r6c1; => r6c1=2

Marty version:

Code:

[r6c1]<>2 [r6c1]=5 [r9c1]<>5 [r9c9]=5 [r9c9]<>1 [r6c9]=1 [r6c9]<>2 [r6c1]=2; => [r6c1]=2
________________________________________________________________________________________

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Sat Dec 13, 2008 12:59 am Post subject:

Quote:

Norm wrote:
mixed ending w-wing

What I see is an ordinary discontinuous loop that doesn't need cells [r7c7] and [r6c7].

this is exactly what it is. instead of an identical pair, we have (2,5) and (1,5) the inference is the same, either 2 or 1 is true. the w-wing connection is the same.

and your discontinous loop is valid also. the chain does not need to go through r7c7 as you pointed out.

what is obvious to me when I look at the strong link on 5's in row 9, is how they connect the (2,5) and (1,5) cells. ding ding ding, alarms go off, the 2 or the 1 is true. simple as that.

oh and Danny, do you realize that your discontinous loop is also a mixed ending M-wing ??

(2=5) - (5) = (5-1) = (1)

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