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 Post subject: Outies
PostPosted: Mon Feb 13, 2012 10:33 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1718
Location: Lethbridge, Alberta, Canada
There are many cases in killer sudokus where one uses the 45 rule to obtain outies which don't "see" each other.

These are frequently 2(1+1) outies where, if their total is an even number, it's possible that they may both be the same number; for example 2(1+1) outies = 6 may be [33].

However there is one special case where the two numbers can't be the same. This is when the two outie cells "see" all the cells of a nonet (this could also apply for a row or a column).

In this position, from my walkthrough for Assassin 215

Image

14. 45 rule on N2 2(1+1) outies R1C3 + R4C5 = 8 = [26/35/71] (cannot be [44] because R1C3 + R4C5 “see” all cells in N2), no 4 in R1C3, no 4 in R4C5

There are several more examples in Assassin 216 and its variants. This was also useful when I solved goooders' Special 1, which has the same cage pattern.

Thanks to Ed for providing the diagram. :)

It is my understanding that, since these cases are fairly rare, SudokuSolver (and possibly other software solvers) isn't programmed to spot this technique. This can result in the SSscore being higher than one would expect, if eliminating the particular pair of identical values needed a lot of work using other methods. goooders' Special 1 was an example of a puzzle having a very high SSscore because of this.


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 Post subject: Re: Outies
PostPosted: Tue Mar 27, 2012 9:26 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1718
Location: Lethbridge, Alberta, Canada
Here is a slightly less obvious case from Assassin 44, Assassin44 V1.5 and Assassin44 V2.

Image

45 rule on N1 2 outies R1C4 + R4C2 = 6 = {15/24}. In this case doubles {33} are not possible because the 21(3) cage at R2C1 cannot contain 3.

Thanks to Ed for also providing the diagram. :)


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