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Is this Coloring or Nishio?

 
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chuckfresno

Joined: 16 Jun 2005
Posts: 39
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PostPosted: Wed Oct 12, 2005 3:37 pm    Post subject: Is this Coloring or Nishio? Reply with quote

Code:
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
6 . . | . . 6 | . . 6
. . 6 | . . . | 6 . .
. . . | . . 6 | . . 6
------+-------+------
. . . | . . . | 6 . .
. . . | . . . | . . .
6 . 6 | . . . | 6 . 6




Coloring r5c3 red(+) and the conjugates blue(-):

Code:
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
 ------+-------+------
-6 . . | . . 6 | . . 6
 . .+6 | . . . |-6 . .
 . . . | . . 6 | . . 6
 ------+-------+------
 . . . | . . . | 6 . .
 . . . | . . . | . . .
 6 .-6 | . . . | 6 . 6


I cannot color any of the cells in box 9, but can see that if the BLUES are true, then they will all be excluded, therefore the blues are false, allowing me to place a 6 in r5c3.


My question -- would this be classified as elimination by coloring or is it simply a Nishio?
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Ruud
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Joined: 17 Sep 2005
Posts: 708
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Location: Netherlands

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PostPosted: Wed Oct 12, 2005 6:42 pm    Post subject: Reply with quote

As far as I know (not being the expert in this field) there are 3 things that you can achieve by colo(u)ring:

1. A candidate is required in both scenarios. It must have that digit.
2. A candidate is eliminated in both scenarios. It cannot have that digit.
3. One of the scenarios creates a contradiction. The scenario cannot be true.

This is a clear case of (3).

I assume you left out a couple of candidates, otherwise r8c8 would have been a single.

If you only tried placing a 6 in r5c3, this would qualify as Nishio.

These techniques tend to overlap each other, just as coloring & fishy cycles & forced chains. It's a bit like quantum mechanics: If you ask a wavy-like question, you get a wavy-like answer, but if you ask a particle-like question, you get a particle-like answer.
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Lummox JR

Joined: 07 Sep 2005
Posts: 202
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PostPosted: Wed Oct 12, 2005 7:57 pm    Post subject: Reply with quote

You're not coloring this grid completely, but only using a single conjugate pair. Coloring can use more than one.

However you have a hidden single in row 7 (or if you like, a pointing pair in box 7, row 9) that means you shouldn't have to use coloring at all. If you place the 6 at (7,7), that leaves another hidden single in row 5, so you can place 6 at (3,5), and then at (1,9). That leaves four candidates that cannot be eliminated by coloring or Nishio.
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chuckfresno

Joined: 16 Jun 2005
Posts: 39
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PostPosted: Wed Oct 12, 2005 11:42 pm    Post subject: Reply with quote

Sorry, typo. I left out a candidate somewhere in row seven. I don't have the original puzzle, but there were no singles.
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