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Unchained?

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keith

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

Posted: Thu Nov 29, 2007 3:29 pm Post subject: Unchained?

Depending on your definition of chains, this one may not need any.

Code:

Puzzle: M4131746sh(10)
+-------+-------+-------+
| . . . | . . . | 4 . . |
| 8 . . | . . . | . . . |
| 4 . . | 3 . . | 5 6 7 |
+-------+-------+-------+
| . 7 . | 8 . . | . . 4 |
| . . . | . . 6 | 2 7 9 |
| . . 3 | . 4 . | . . . |
+-------+-------+-------+
| . . . | . 2 . | . . . |
| . . 6 | 4 . 8 | 7 3 . |
| . 2 . | . 5 . | 6 9 . |
+-------+-------+-------+

It is much tougher than this site's Very Hards.

Keith

nataraj

Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

Posted: Thu Nov 29, 2007 4:00 pm Post subject: Re: Unchained?

keith wrote:

Depending on your definition of chains, this one may not need any.

In my book, coloring (even multi-coloring) is not "chains" (but of course the reasoning uses inference chains, what else). So in that sense removing some "1"s, "2"s and "5"s got me quite far. But here:

Code:

+--------------------------+--------------------------+--------------------------+
| 279 36 1579 | 29 67 159 | 4 8 13 |
| 8 36 157 | 15 67 4 | 9 2 13 |
| 4 19 129 | 3 8 129 | 5 6 7 |
+--------------------------+--------------------------+--------------------------+
| 6 7 129 | 8 19 259 | 3 15 4 |
| 15 4 8 | 15 3 6 | 2 7 9 |
| 259 159 3 | 29 4 7 | 8 15 6 |
+--------------------------+--------------------------+--------------------------+
| 379 8 79 | 6 2 39 | 1 4 5 |
| 59 159 6 | 4 19 8 | 7 3 2 |
| 13 2 4 | 7 5 13 | 6 9 8 |
+--------------------------+--------------------------+--------------------------+

I did need chains. Starting with the useless xy wing pivot r8c1 (19-59-15) I kept looking around. And found these babies:
'51'(51)='13'(91)='31'(96)='19'(85)='95'(81)
'76'(25)='63'(22)='31'(29)='15'(24)='51'(54)='15'(51)='59'(81)='97'(73)
'95'(81)='51'(51)='13'(91)='31'(96)='19'(85)

There are 5 cells that form a loop: -15-15-19-19-59-
How does this help?

(edit. P.S.: another coloroing elimination later on "9"s solved the puzzle for me)

ravel

Joined: 21 Apr 2006
Posts: 536

Posted: Thu Nov 29, 2007 4:24 pm Post subject:

There is a very simple forcing chain solving the puzzle:

Code:

*------------------------------------------------*
| 12579 36 1579 | 29 67 B159 | 4 8 13 |
| 8 36 157 |A15 67 4 | 9 2 13 |
| 4 19 129 | 3 8 -129 | 5 6 7 |
|-------------------+---------------+------------|
| 6 7 1259 | 8 19 1259 | 3 15 4 |
| 15 4 8 | 15 3 6 | 2 7 9 |
| 1259 159 3 | 29 4 7 | 8 15 6 |
|-------------------+---------------+------------|
| 379 8 79 | 6 2 B39 | 1 4 5 |
| 159 159 6 | 4 19 8 | 7 3 2 |
| 13 2 4 | 7 5 B13 | 6 9 8 |
*------------------------------------------------*

In box 5 the 5 can be in r5c4 (=> r2c4=1) or r4c7 (=> r3c7=2)
In both cases r3c7 cannot be 1.

It can be done with an ALS too (x=5, z=1)

nataraj

Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

Posted: Thu Nov 29, 2007 4:59 pm Post subject:

ALSs: chainless in the extreme - by any definition. very elegant.

I tried to use your ALS and avoid (color and other) chains, but this is where it stops:

Code:

+--------------------------+--------------------------+--------------------------+
| 2579 36 2579 | 29 67 15 | 4 8 13 |
| 8 36 57 | 15 67 4 | 9 2 13 |
| 4 19 129 | 3 8 29 | 5 6 7 |
+--------------------------+--------------------------+--------------------------+
| 6 7 1259 | 8 19 1259 | 3 15 4 |
| 15 4 8 | 15 3 6 | 2 7 9 |
| 1259 159 3 | 29 4 7 | 8 15 6 |
+--------------------------+--------------------------+--------------------------+
| 379 8 79 | 6 2 39 | 1 4 5 |
| 159 159 6 | 4 19 8 | 7 3 2 |
| 13 2 4 | 7 5 13 | 6 9 8 |
+--------------------------+--------------------------+--------------------------+

edit : I see it now. xwing on 2

Last edited by nataraj on Thu Nov 29, 2007 5:12 pm; edited 2 times in total

keith

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

Posted: Thu Nov 29, 2007 4:59 pm Post subject:

In the posted position:

Code:

+----------------+----------------+----------------+
| 279 36 1579 | 29 67 159 | 4 8 13 |
| 8 36 157 | 15 67 4 | 9 2 13 |
| 4 19 129 | 3 8 129 | 5 6 7 |
+----------------+----------------+----------------+
| 6 7 -129 | 8 19 259# | 3 15@ 4 |
| 15@ 4 8 | 15# 3 6 | 2 7 9 |
| 259 159 3 | 29 4 7 | 8 15 6 |
+----------------+----------------+----------------+
| 379 8 79 | 6 2 39 | 1 4 5 |
| 59 159 6 | 4 19 8 | 7 3 2 |
| 13 2 4 | 7 5 13 | 6 9 8 |
+----------------+----------------+----------------+

@@ is a W-wing connected by the link ## on <5>. It takes out <1> in r4c3.

After some cleaning up, coloring on <9> solves R8C1 as <5>, and the puzzle is done.

Keith

Earl

Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

Posted: Thu Nov 29, 2007 6:50 pm Post subject: Chains

I thought I had a simple solution, but it was just dumb luck. Earl Last edited by Earl on Thu Nov 29, 2007 7:51 pm; edited 2 times in total

Earl

Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

Posted: Thu Nov 29, 2007 7:48 pm Post subject: Re: chains

SORRY - my error - Senior moment ! Earl

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