SudokuSolver Forum
http://www.rcbroughton.co.uk/sudoku/forum/

Nishio? edit: No..XY-X Chain
http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=8&t=719		 Page 1 of 1
Author:  Ed [ Sun Mar 21, 2010 2:22 am ]
Post subject:  Nishio? edit: No..XY-X Chain
I'm not exactly sure what this technique is. At first I thought it was a Killer Empty Rectangle (ER) but it involves two digits so perhaps not. Nishio? Please post if you know what it is. I really enjoyed finding it so wanted to share it. It's from my walkthrough for A21v1 here. What drew me to see it was that both spots involved the same two digits.

ImageNOTE: the blue highlights all the 7s.

11. r7c89 = [78/86] = [7/6] -> {67} blocked from 13(2)n6 since there is no 7 in r123c7


11a. another way of seeing this:
i. {67} in r56c9 -> r7c9 = 8 -> r7c8 = 7:
ii. {67} in r56c9 -> 7 in n3 only in c8, 7 locked for c8: but this means two 7s in c8
11b. yet another way of seeing this: (this one courtesy of Andrew)
i. If r7c89 = [78] -> 7 in n3 in c9 -> no 7 in 13(2) at r56c9 -> {67} blocked
ii. If r7c89 = [86] -> {67} blocked from 13(2) at r56c9

Cheers
Ed
Author:  mhparker [ Mon Mar 22, 2010 9:06 pm ]
Post subject:  Re: Nishio?
Ed wrote:
I'm not exactly sure what this technique is. At first I thought it was a Killer Empty Rectangle (ER) but it involves two digits so perhaps not. Nishio?

Actually, it involves three digits (6, 7 and 8). There's AFAIK no special name for it, because it's not a homogeneous chain based on a single technique. Instead, it's a hybrid of an XY-chain and an X-cycle. For that reason, I personally would just use the generic term and call it an AIC (Alternating Inference Chain), expressible in Eureka notation as follows:

(6=8)r7c9-(8=7)r7c8-(7)r123c8=(7)r123c9

In other words, either r7c9 contains a 6, or r123c9 contains a 7 => no {67} in 13(2)c9.

Nishio is something quite different. I'll try to post an example of that on this thread soon. In the meantime, well done for finding the chain and thanks for sharing it with us, Ed! :D
Author:  mhparker [ Wed Mar 24, 2010 10:27 pm ]
Post subject:  Re: Nishio?
I wrote:
Instead, it's a hybrid of an XY-chain and an X-cycle.

Hi Ed, I've just found out that JSudoku refers to these types of hybrid chains as XY-X-Chains. I don't know how standardized that is, but I can't think of any better nomenclature and it seems (from my quote above) to be a very logical suggestion to me. I for one will therefore also be using this terminology in the future.
Author:  Ed [ Sun Mar 28, 2010 3:35 am ]
Post subject:  Re: Nishio?
Thanks very much Mike for your helpful explanation. It is more complicated than I thought. This reminded me of another example of what looks an XY-X chain (SS actually called it an "XY Chain").

From A170 v1.5, Afmob's optimized WT (here) step 3h with all the 9's highlighted:

Image
4. XY-X Chain [edit on name following udosuk]-> no 7 in r4c7. Like this.
4a. If r3c7 is not 7 it's 8. When it's 8 -> r3c3 = 9 -> r4c4 = 8 -> 9 in r4 must be in r4c7 -> no 7 in r4c7
4b. If r3c7 = 7 -> no 7 in r4c7


ALT ways of expressing it courtesy of udosuk:
"r4c47 form a strong link of 9 on r4.
Therefore r34c7=[87] would force r3c3+r4c4=[99], contradiction.
Hence r4c7 can't be 7."

"(Or alternatively, one of r3c3+r4c4 must be 8, forcing r3c7=7 or r4c7=9, so r4c7<>7 no matter what.)"

I quite like it.

Cheers
Ed
Page 1 of 1 All times are UTC
Powered by phpBB® Forum Software © phpBB Group
https://www.phpbb.com/