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 Post subject: CPE
PostPosted: Wed Jun 17, 2009 10:26 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Common Peer Elimination (CPE) was first introduced on the forum (the term at least) by Mike (mhparker) in A46 and A49v2. When a candidate in one house is the peer of all of that candidate in another house, then the candidate in the first house can be eliminated. For regular killers, this needs a cage crossing over into the first house to work. For diagonal killers, the diagonals can act to create a common peer. Jigsaw killers are hilarious for really weird CPE!

A86 is a classic example of CPE because of it's importance to the solution. I'll use Mike's WT to illustrate.

Image

1. Outies C89: R14C7 = 3(2) = {12}, locked for C7
1a! -> no 1,2 in R23C8+R12C9 (CPE)


Image

Mike has a really nice cell-cloning step so can't resist including that.
3. R3C9 and R4C7 must contain the same digit, because they both see R1C7
3a. -> this digit (1 or 2) must be constrained to C8 within N9
3c. -> R9C8 = {12}


Image

The pic above highlights all the 1's in the grid.
7. 1 in N5 locked in C4 -> not elsewhere in C4
7a. no 1 in R5C3 (NOTE: this is a CPE move)

Now the puzzle breaker
8. 1 in N4 locked in R56C12
8a. -> no 1 in R7C1 (CPE)

9. Hidden single (HS) in R7 at R7C6 = 1

Many thanks to Andrew for making good suggestions, including to have this thread.

Cheers
Ed


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 Post subject: Re: CPE
PostPosted: Sun Jan 17, 2010 7:20 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks Ed for an excellent start to this thread!

Ed wrote:
Common Peer Elimination (CPE) was first introduced on the forum (the term at least) ...
This technique is also known by other names including Pointing Pairs and Pointing Cells.


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 Post subject: Re: CPE
PostPosted: Sun Jan 17, 2010 7:34 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
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Location: Lethbridge, Alberta, Canada
This post is to emphasise the importance of identifying all appropriate cells when using CPE.

When I started solving A165 this part of the diagram appeared after doing Prelims.

Image

I immediately spotted the obvious eliminations of 1,3 from R4C6 and R5C7 and subsequently got stuck.

It was only when I came back to this puzzle that I realised that both cells of the 4(2) cage at R4C7 "see" several more cells. The full CPE is no 1,3 in R4C456 + R5C78. For this puzzle eliminating 1,3 from R5C8 proved to be key to solving it.

It is, of course, equally important to make sure that you don't apply the CPE to cells where it isn't valid. Spotting cells which don't "see" all the cells of a large cage can lead to other solving techniques, which are covered elsewhere in this Killer Techniques forum.

Thanks Ed for providing the diagram!


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 Post subject: Re: CPE
PostPosted: Sun Jan 17, 2010 7:43 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
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Location: Lethbridge, Alberta, Canada
This is a more unusual example of a CPE, using a diagonal of a Killer-X.

It is taken from A186. In my walkthrough I had reached the following position after step 19.

Image

Ed pointed out that I could have used 2 on D/ only in R3C7 + R5C5 + R7C3, CPE no 2 in R7C7, clean-up: no 9 in R3C3 (because R3C3 + R7C7 = 11 from 45 rule on D\) leading to R2C2 = 9 (hidden single on D\) slightly earlier than in my solving path.

Thanks Ed for providing the diagram!


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