colouring disconnected chains ;)

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colouring disconnected chains ;)

Postby speter » Tue May 23, 2017 2:39 am

The puzzle below is from sudoku-wiki (http://www.sudokuwiki.org/Jelly_Fish_Strategy).
I was trying to work out the jelly fish example and got distracted by something else...

When I studied candidate 6, I found a number of disconnected chains!
My questions is: can I colour the disconnected chains!?
In other words r1c2 - r3c2 and r2c6 - r3c6 are not joined, but would it be correct to colour r3c2 and r3c6 opposing colours!?

If I can 'colour' them, I think it would allow me to eliminate candidate 6 from: r1c9, r2c8, r3c8 & r3c9.

Image
Code: Select all
. . 1 | 7 5 3 | 8 . .
. 5 . | . . . | . . 7
7 . . | 8 9 . | 1 . .
------+-------+------
. . . | 6 . 1 | 5 7 .
6 2 5 | 4 7 8 | 9 3 1
. 1 7 | 9 . 5 | 4 . .
------+-------+------
. . . | . 6 7 | . . 4
. 7 . | . . . | . 1 .
. . 6 | 3 . 9 | 7 . .


[edited to replace photobucket image share with imgur image share]
Last edited by speter on Wed Jul 05, 2017 7:27 am, edited 1 time in total.
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Re: colouring disconnected chains ;)

Postby champagne » Tue May 23, 2017 9:06 am

IMO, the way you are doing it is very dangerous.
It pushes you to believe that 2 cells having different colors are "one true" "one false" and this is not established.

For example start with ric2 false. you have

r1c2 false
r3c2 true (bi-value)
r3c6 false
r2c6 true (bi-value)
r2c7 false
r7c7 true (bi-value)
r7c9 false
but here the chain is cut. You can not continue with r6c9 true, this is not a bi-value.
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Re: colouring disconnected chains ;)

Postby speter » Tue May 23, 2017 10:45 am

Thanks for the reply.
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Re: colouring disconnected chains ;)

Postby JasonLion » Tue May 23, 2017 1:17 pm

What you are trying to do is very similar to Multi-Colors or X-Colors. The rules are more complex than for Simple Coloring, but it is possible to make progress in this direction. Alternatively, you could go all the way to Alternating Inference Chains, which are more complex still, but more generally useful.
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