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 Post subject: Cell-cloning
PostPosted: Fri Jul 10, 2009 8:53 pm 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Cell-cloning is, in my recollection, a name coined by udosuk. The first time he used it on the Assassin forum is here in A122 v1.5. Mike used the move in A86, his step 3, as shown here.

1) The easiest form of cell-cloning is from innie outie difference (IOD). If the difference between one outie and one innie is 0, then the two cells must be the same. If candidates get eliminated from one cell, they can be eliminated from the other as well. If one cell gets placed, the other can be placed.

2) Sometimes, the cage structure allows a cell-clone. A classic example of this is is by Afmob in A138. It uses an 8-cell cage with one cell that see all cells bar one in another nonet.

Image

Afmob wrote:
1e) ! R7C5 = R4C6 since R7C5 sees all of N5 but R4C6 -> R7C5 = (46)
The next step is well worth a mention with a nice implied blocker move. You can still see it in the diagram above.
Afmob wrote:
1f) ! R7C5 = R4C6 = 4 since they see all 6 of 10(3)
These two moves crack the puzzle.

3) Next, cell-cloning can result from a combination of the "45" rule and cage structure. This comes from my walkthrough for JFFK 1 here.

Image

Ed wrote:
1. "45" c1234: 1 outie r7c5 + 4 = 1 innie r2c4
1a. r7c5 = 1,2.3,5
1b. r2c4 = 5,6,7,9 (note: the diagram above mistakenly has an 8 still in r2c4. Ooops)

2. r7c5 "sees" all cells in c4 either directly (through the same 41(8)n1 cage or n8) or indirectly though i/o c1234 (step 1) EXCEPT r1c4
2a. since r2c4 cannot equal r7c5 (step 1) -> r1c4 = r7c5 = (1235) (cell-clone)
2b. r9c4 = 4 (hsingle c4)
BTW: manu and Andrew got this same placement in r9c4 inversely, by what we could call anti-cloning:
r9c4 cannot equal any candidate in the 41(8) cage since it sees seven of the cells and the one cell it can't see (r3c3) cannot be the same because of the IOD C123
-> r9c4 must be the one candidate missing from a 41(8)
-> r9c4 = 4

This type of cell-clone is very hard to see when there are several cages involved. See manu's example here (see 1 & 2 at the bottom of his post). This move is dependent on proving that most other cells in a house CANNOT share the same digit with cells in another house. See my follow up post on Large IOD here.

There are at least three other types of cell-cloning, from combinations, from locked candidates combined with the IOD and from IOE. They can wait for a separate post.

Cheers
Ed


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 Post subject: Re: Cell-cloning
PostPosted: Thu Dec 17, 2009 2:43 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
In a PM to me, manu wrote:
I have made the cage patterns of both JFFK1 and JFFK3 aiming at using this following particular technique :
if a cell C is different of all cells of a cage X(8) (it sees all of them or from IO difference elimination), then C=45-X
(can be used for cage X(7) or X(6), but then, one only obtains elimination of candidates for cell C)
If you haven't yet tried JFFK1 and JFFK3, then have a go at them, remembering what manu has said above.

Many of manu's puzzles are based on "cloning". Smooth A180, A180 and Børge's variant A180 V1.5 are excellent examples to try. In the case of A180 V1.5, manu and I used different sets of "clones" for our solutions.


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