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Regular Samurai #16
http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=16&t=230		 Page 2 of 2
Author:  enxio27 [ Tue Oct 26, 2010 1:23 am ]
Post subject:  Re: Regular Samurai #16
Børge wrote:
Can you see the elimination(s) now?


I had the right cells, but it took me a while to find one elimination (5 in R4C1). We'll see how far that gets me.

UPDATE: OK, that did the trick! Thanks, Børge!

I'm just not sure I could recognize a similar scenario if I saw one again. Was that a Y-wing or an XY-X chain you showed me? I can't seem to find either one (at least by those names) in Tom Davis' monograph.
Author:  Børge [ Tue Oct 26, 2010 2:51 pm ]
Post subject:  Re: Regular Samurai #16
The correct elimination is r6c4 <> 5 using the following Y-Wing:

Image


Here one possible general description of a Y-Wing:
  1. If you in a house can place the digit X in only two cells, let's call these two cells W1 and W2.
  2. If W1 sees a cell W3 with only the two possible digits X and Y, and W2 sees a cell W4 with also only the two possible digits X and Y, and W3 <> W4
    THEN the digit Y can be eliminated from all cells, which see both W3 and W4.

In the above Y-Wing:
W1 = r4c5
W2 = r4c8
W3 = r5c4
W4 = r6c8
Author:  enxio27 [ Tue Oct 26, 2010 3:14 pm ]
Post subject:  Re: Regular Samurai #16
Børge wrote:
The correct elimination is is r6c4 <> 5 using the following Y-Wing:

Now I see it! I must have taken a harder path using all five of those highlighted cells to eliminate the 5 in r4c1.

Quote:
Here one possible general description of a Y-Wing:

Thanks for that! I'll have to study it out some more so I can get a handle on it to recognize it again.

Out of curiosity, do I really need the r4c58 to eliminate the 5 in r6c4?

BTW, did you go back and delete part of your above post? I could have sworn there was some description of 2-string kite and another technique being special cases of the Y-wing, but now it's gone.
Author:  Børge [ Tue Oct 26, 2010 3:44 pm ]
Post subject:  Re: Regular Samurai #16
enxio27 wrote:
Now I see it! I must have taken a harder path using all five of those highlighted cells to eliminate the 5 in r4c1.
You can use a 4 cell chain (XY-X-Chain I think, getting a bit rusty so I have to think it over) r4c8 -> r6c8 -> r6c4 -> r4c5 to prove that r4c1 <> 5.
Here a Y-Wing, which proves that r4c1 <> 5
Hidden Text:
Image

enxio27 wrote:
Out of curiosity, do I really need the r4c58 to eliminate the 5 in r6c4?
If you have any suggestions on how to eliminate the 5 in r6c4 without using r4c58, I am all ears!


enxio27 wrote:
BTW, did you go back and delete part of your above post? I could have sworn there was some description of 2-string kite and another technique being special cases of the Y-wing, but now it's gone.
YES, I did go back and delete part of my above post. I wrote that Two-String Kite and Skyscraper are special cases of the general Y-Wing. This is of course absolute rubbish. As I said above, getting a bit rusty from not having solved sudokus in a while.
Author:  Børge [ Tue Oct 26, 2010 6:09 pm ]
Post subject:  Re: Regular Samurai #16
enxio27 wrote:
I had the right cells, but it took me a while to find one elimination (5 in R4C1).
enxio27 wrote:
I must have taken a harder path using all five of those highlighted cells to eliminate the 5 in r4c1.

You probably used the following chain, AFAIK called an XYT-Chain:

Image



This is the more formal XY-X-Chain:

Image
Author:  enxio27 [ Tue Oct 26, 2010 8:35 pm ]
Post subject:  Re: Regular Samurai #16
Børge wrote:
If you have any suggestions on how to eliminate the 5 in r6c4 without using r4c58, I am all ears!

Never mind! Just my faulty logic again. :oops:

enxio27 wrote:
YES, I did go back and delete part of my above post.

Ok, just making sure I'm not going crazy! LOL! :drunk:

Quote:
You probably used the following chain, AFAIK called an XYT-Chain:

Yes, that's it!

The more advanced the techniques get, the longer it's taking me to work out the logic behind them. I'm still wrapping my brain around the Y-wing.
Author:  Børge [ Tue Oct 26, 2010 8:57 pm ]
Post subject:  Re: Regular Samurai #16
enxio27 wrote:
I'm still wrapping my brain around the Y-wing.
Brain exercise is almost always a good thing.

The logic behind the Y-Wing is fairly simple. Spotting one is a total different story.

Again my definition of a Y-Wing:
  1. If you in a house can place the digit X in only two cells, let's call these two cells W1 and W2.
  2. If W1 sees a cell W3 with only the two possible digits X and Y, and W2 sees a cell W4 with also only the two possible digits X and Y, and W3 <> W4
    THEN the digit Y can be eliminated from all cells, which see both W3 and W4.

1. says that in a given house the digit X can only be placed in one of the two cells W1 or W2.
   There are no other possibilities.
2. says:
  • Both W1 and W2 sees a cell having only the two possible digits X and Y,
    i.e. W1 sees W3 with only the two possible digits X and Y
    and  W2 sees W4 with only the two possible digits X and Y.
  • Then the following must be true:
    If W1=X -> W3=Y -> all cells that W3 sees <> Y.
    If W2=X -> W4=Y -> all cells that W4 sees <> Y.
    This means that the digit Y must be in either W3 or W4.
    Hence all cells that see both W3 and W4 <> Y.
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