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Remote linked pairs through overlapping naked triples

 
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Ruud
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Joined: 17 Sep 2005
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Location: Netherlands

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PostPosted: Sun Oct 09, 2005 9:34 pm    Post subject: Remote linked pairs through overlapping naked triples Reply with quote

I found some behaviour that we might utilize in a solving technique, but since I haven't implemented coloring yet, I'm not sure how we can use it to its full extent.

Here's the example:

Code:
a b .|. . .|c . .
. . .|. . .|. . .
. . d|. . .|. . .
-----|-----+-----

Now when a-b-c are a naked subset, and a-b-d is also a naked subset with the same digits, c and d must be the same digit. That is because any value assigned to c would make a-b a naked pair for the remaining 2 values. Same story when you choose any value for d.

We probably need something else conjugated with c or d to really use this, but one thing can already be deducted. When either c or d have less than the full 3 candidates in the subset, the other one can have no more than those 2 candidates. Even more: when c and d share only one of the 3 digits in the subset, both c and d must have that value.

My questions:

1. Is this theory correct?
2. Can it happen in a real puzzle? (a working sample would be nice)
3. If 1. and 2. are answered with yes, how can we further utilize this connection?
4. Did I reinvent the somaniest wheel?
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