What's this?

Advanced methods and approaches for solving Sudoku puzzles

What's this?

Postby evert » Mon Mar 06, 2006 11:18 pm

In the following pattern R2C8 and R7C9 allways have the same value.
I used some kind of combination between XY wing and this to exclude "<9>"

Code: Select all
 *--------------------------------------------------------------------*
 |                      |                      |                      |
 |                      |               <9>    |        79     789    |
 |                      |                      |               789    |
 |----------------------+----------------------+----------------------|
 |                      |                      |                      |
 |                      |                      |                      |
 |                      |                      |                      |
 |----------------------+----------------------+----------------------|
 |                      |               37     |               79     |
 |                      |                      |                      |
 |                      |               39     |                      |
 *--------------------------------------------------------------------*
evert
 
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Postby Carcul » Mon Mar 06, 2006 11:32 pm

Hi Evert.

I would made that deduction with a discontinuous nice loop:

[r2c6]-9-[r9c6]-3-[r7c6]-7-[r7c9]-9-[r2c9|r3c9]-7-[r2c8]-9-[r2c6], => r2c6<>9.

Regards, Carcul
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Re: What's this?

Postby ronk » Mon Mar 06, 2006 11:42 pm

evert wrote:In the following pattern R2C8 and R7C9 allways have the same value.
I used some kind of combination between XY wing and this to exclude "<9>"

You can look at that as a chain of almost-locked-sets:
A = {r79c6} = {379}, where r9c6<>9 implies r7c6=7
B = {r7c9} = {79}
C = {r23c9} = {789}, where r23c9<>9 implies r23c9=78 (naked pair)
D = {r2c8} = {79}

Chained: if r9c6<>9 then r2c8=9, and v.v.

Ron
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Location: Southeastern USA

Re: What's this?

Postby aeb » Tue Mar 07, 2006 12:03 am

evert wrote:In the following pattern R2C8 and R7C9 always have the same value.
I used some kind of combination between XY wing and this to exclude "<9>"

Code: Select all
 *--------------------------------------------------------------------*
 |                      |                      |                      |
 |                      |               <9>    |        79     789    |
 |                      |                      |               789    |
 |----------------------+----------------------+----------------------|
 |                      |                      |                      |
 |                      |                      |                      |
 |                      |                      |                      |
 |----------------------+----------------------+----------------------|
 |                      |               37     |               79     |
 |                      |                      |                      |
 |                      |               39     |                      |
 *--------------------------------------------------------------------*

You see a set of size 6 with digit candidates 3789 with maximal multiplicities 1213 for a total of 7 so any outside choice that would reduce the total by 2 can be eliminated. And your <9> does reduce the max multiplicity of 9 in the set from 3 to 1.
aeb
 
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Postby Myth Jellies » Sat Mar 11, 2006 2:04 am

aeb, I have to say that I like the way that your concept of a single set and multiplicities simplifies ALS work. I think you ought to start your own thread on the subject.
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Postby aeb » Sat Mar 11, 2006 2:36 pm

Myth Jellies wrote:aeb, I have to say that I like the way that your concept of a single set and multiplicities simplifies ALS work. I think you ought to start your own thread on the subject.

OK - done.
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