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Properties of Colors/Coloring

 
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daj95376

Joined: 05 Feb 2006
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PostPosted: Fri Jun 23, 2006 11:50 pm    Post subject: Properties of Colors/Coloring Reply with quote

According to the search engine, there are 127 message threads containing colors OR coloring. I'm hoping someone will be kind enough to save my poor eyes a lot of reading to get a couple of questions answered.

The following properties for simple Colors/Coloring were extracted -- and slight reworded by me -- from the Help facility in Simple Sudoku.

Quote:
Whenever two cells in a conjugate chain have the same color and also share the same unit, that color must be the false color since each unit can legitimately have atmost one of each color. (This means that the candidate can be eliminated in the false-colored cells.)

Also, whenever the candidate is in a cell that's outside the chain but is a buddy to two alternately colored cells in the chain, that 'non-chain' candidate can be excluded.


Now, the first thing I suspect is that it's possible for these two conditions to exist simultaneously. Therefore, it's critical that the first rule takes precedence. Does anyone disagree?

The next thing I suspect is that for Colors/Coloring to work, there must be at least one block where a conjugate pair in the chain are not in the same row/column. I call this the diagonal property. Does anyone disagree?

Finally, how should I report this technique is a solution listing? I'd like to be as informative as possible while still being compact.

TIA!!!
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rkral

Joined: 21 Oct 2005
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PostPosted: Sat Jun 24, 2006 10:16 am    Post subject: Re: Properties of Colors/Coloring Reply with quote

daj95376 wrote:
I suspect is that it's possible for these two conditions to exist simultaneously. Therefore, it's critical that the first rule takes precedence. Does anyone disagree?

Disgree. The exclusion of an uncolored cell that is a buddy of two alternatively colored cells depends upon the fact that exactly one of two colors ultimately represents the true positions of a digit. It matters not that we might have first known which color was true.

daj95376 wrote:
there must be at least one block where a conjugate pair in the chain are not in the same row/column. I call this the diagonal property. Does anyone disagree?

Agree and disagree. For exclusions via "simple coloring" -- the coloring of a single conjugate chain of a single digit -- that is true. For exclusions via "multiple-coloring" -- the coloring of two or more conjugate chains of a single digit -- that is not true. An x-wing is a trivial example of the latter.

daj95376 wrote:
Finally, how should I report this technique is a solution listing?

Good question, but I have no good anxwer. You could start with Angus Johnson's rule numbers, I suppose.
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daj95376

Joined: 05 Feb 2006
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PostPosted: Sat Jun 24, 2006 3:19 pm    Post subject: Reply with quote

rkral,

Thanks for the input!!! I'll have to review my implementation options in light of it.
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angusj
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Joined: 18 Jun 2005
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PostPosted: Sun Jun 25, 2006 5:22 am    Post subject: Re: Properties of Colors/Coloring Reply with quote

daj95376 wrote:
Now, the first thing I suspect is that it's possible for these two conditions to exist simultaneously. Therefore, it's critical that the first rule takes precedence. Does anyone disagree?

You could reasonably argue that spotting a candidate that meets the first rule is more likely before spotting a candidate that meets the second. (I'm now quite out of practice in this so I can't be more emphatic about that.) However, it's certainly not critical, in fact it doesn't matter at all which technique is applied first.
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