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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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 Posted: Thu Sep 17, 2009 3:47 pm Post subject: BUG+X |
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Yesterday I found myself with a BUG+2, except one of the cells contained four candidates rather than three. I didn't know what to do, so I just moved on to other techniques to finish.
So my question is: whether it's a +1 or +2, is there something that can be done with a four-candidate cell within the BUG+ technique? |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Thu Sep 17, 2009 4:49 pm Post subject: Re: BUG+X |
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| Marty R. wrote: |
So my question is: whether it's a +1 or +2, is there something that can be done with a four-candidate cell within the BUG+ technique? |
The answer is: yes to the second part (a cell with two extra candidates is already "plus two").
Let me go back to the so called "unique rectangles" (URs). In URs, the "Deadly Pattern" is a rectangle of 4 cells, each with the same two candidates.
This Deadly Pattern (DP) allows for more than one solution and is therefore invalid. Since the creator of the puzzle guarantees that the solution is unique, at least one of the cells must contain a different candidate.
Same with BUG. This "Big Universal Grave" is just another DP. And in order to avoid the DP, at least one cell must contain a candidate that is not part of the DP.
In BUG+1 there is only ONE such extra candidate. Therfore the extra candidate immediately solves the puzzle.
In BUG+x situations, all we know is that at least one of the extra candidates (those not in the deadly pattern) must be correct.
IMHO, it does not matter whether they are in x different cells.
So, if there is a BUG+2 in such a way that one cell has two extra candidates (apart from the DP), we know that one of them must be true.
If there are three extra candidates in two cells, each one of them breaks the deadly pattern, so we know at least one of the three must be correct.
It depends on the puzzle, how useful this information is. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Sep 17, 2009 9:10 pm Post subject: |
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| OK, Nataraj, got ya. Thanks. |
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