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Nightmare April 6 06: A new trick for an old dog!

 
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keith



Joined: 19 Sep 2005
Posts: 3182
Location: near Detroit, Michigan, USA

PostPosted: Thu Apr 06, 2006 10:53 pm    Post subject: Nightmare April 6 06: A new trick for an old dog! Reply with quote

Here is an interesting new (for me) technique that I learned here:

http://www.sudoku.com/forums/viewtopic.php?t=3326

It fits my bill: Easy to spot, easy to understand, and potentially very powerful. You can read the explanation at the link given above, but let me ask: How did you do on today's (Apr 6) SudoCue Nightmare?

After using the basic techniques, you get here:

Code:


+-------------------+-------------------+-------------------+
| 15    4     1259  | 3679  35679 567   | 1236  8     169   |
| 8     259   7     | 369   3569  1     | 2346  2349  469   |
| 16    3     169b  | 8     2     4     | 7     19a   5     |
+-------------------+-------------------+-------------------+
| 2     157   13458 | 167   1567  9     | 13468 134   14678 |
| 147   6     149d  | 2     8     3     | 14    5     1479c |
| 1357  1579  13589 | 4     1567  567   | 1368  139e  2     |
+-------------------+-------------------+-------------------+
| 9     125   12356 | 136   4     26    | 1258  7     18    |
| 1467  127   1246  | 5     167   8     | 9     124   3     |
| 13457 8     12345 | 1379  1379  27    | 1245  6     14    |
+-------------------+-------------------+-------------------+



Now, the software I use suggests: "Guess!" (Japanese translation: ”Nishio!")

However, take a look at R3 and R5. The possibility <9> occurs only twice in each row, so the pairs of squares in each Row each have a "strong" link. They are (b-a, d-c). Also, (b) and (d) line up in a column. (If (a) and (c) also lined up in a column, you'd have an X-wing, but they don't, and you don't.)

This is simply the pattern to look for: Two strong links that line up at one end. (If you're looking for X-wings, you're doing this already.)

So what? Well, one of the squares labeled (a) or (c) must be <9>! So, in this example, R6C8 (e) is not <9>, R5C9 (c) is <9>, and this pretty much breaks the logjam. I got through the rest with a couple of XY-wings and some simple coloring.

What? The proof is like this: If (a) is <9>, (a) is <9>. If (a) is not <9>, (b) is <9>, (d) is not <9>, and (c) is <9>.

I am sure there is a name for this, and I am sure it is a special case of some general method. But, I have not seen it explained this way before. (If you show me the chain I can see it, but please tell me how to find it on my own!)

Best wishes,

Keith


Last edited by keith on Fri Apr 14, 2006 5:09 am; edited 1 time in total
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Fri Apr 07, 2006 3:41 am    Post subject: Reply with quote

I was glad to see you publicise this useful device. I think of it as a fork.

The recipe is two strong links (the tines) arranged so that one end of one tine is an associate of one end of the other. The base candidate, X, can be eliminated from any cell associated with both the other two ends. You describe the logic clearly.

It is an extremely flexible tool in that the tines can be conjugates in two boxes, a box and a column, a row and a column…. All nine possibilities arise. This example eliminates X from r2c1:
Code:
-------------------------
| . . . | . . . | . . . |
| . . . | . . . | . . X |
| . . . | . . . | . . . |
-------------------------
| . . . | . . . | . . . |
| . . X | . . . | . . X |
| X . . | . . . | . . . |
-------------------------
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
-------------------------

The cells marked with X are the only places for X in box 4 and column 9.

In my opinion ithe "fork" should be in the manuals just before the X-wing, of which it is a building block.

I think the idea has suffered from being a part of so many more complicated techniques. It is all there is in a turbot fish, for example. Multocolouring produces the same result as a fork and more besides. Your own example, on two rows, is also a finned X-wing although, again, the finned X-wing offers more possibilities.

My reason for avoiding these names is mainly because they cover wider concepts (except for the turbot fish, which I resist because it is not a fish at all). In addition these more advanced methods do not relate very well to the grouped fork. Here one of the “conjugate cells” is actually several cells in a box. Consider:
Code:
-------------------------
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
-------------------------
| . X X | . . . | . . X |
| . . . | . . . | . . . |
| X . X | . . . | . . X |
-------------------------
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
-------------------------

The places for X in rows 4 and 6 are confined to box 4 or column9. The same logic eliminates X from the rest of row 9.

The "Nightmare" program prouces plain forks frequently. The grouped fork does not seem to be progammed into setters as yet though on or two have cropped up.

Keep up the good work!

Steve
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ravel
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PostPosted: Fri Apr 07, 2006 10:01 am    Post subject: Reply with quote

Just for giving the history:
This technique was introduced by Nick70 already in July 05 as "turbot fish", later on it was integrated in "advanced coloring" (comprising also 3 and more strong links). But Havard's explanation is obviously the best.

BTW, under all the new techniques of the last year IMHO there are only 3, that are both easy to spot and rather common to apply in puzzles: Turbot fish, xy(z)-wing and unique rectangles.
Rather common, but harder to spot, are finned x-wings. Easy to spot, but rather rare is the BUG pattern with only 1 cell having 3 candidates.
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Fri Apr 07, 2006 1:55 pm    Post subject: "Nishio" isn't guessing Reply with quote

Keith wrote:
Now, the software I use suggests: "Guess!" (Japanese translation: ”Nishio!")

Thanks for the very clear explanation of "multi-coloring," Keith. This puzzle is also a good example of "Nishio," which in this case just amounts to looking at the binary chains you've located the other way round.
Code:
+-------------------+-------------------+-------------------+
| 15    4     1259  | 3679  35679 567   | 1236  8     169   |
| 8     259   7     | 369   3569  1     | 2346  2349  469   |
| 16    3     169   | 8     2     4     | 7     19   5      |
+-------------------+-------------------+-------------------+
| 2     157   13458 | 167   1567  9     | 13468 134   14678 |
| 147   6     149   | 2     8     3     | 14    5     1479  |
| 1357  1579  13589 | 4     1567  567   | 1368  139*  2     |
+-------------------+-------------------+-------------------+
| 9     125   12356 | 136   4     26    | 1258  7     18    |
| 1467  127   1246  | 5     167   8     | 9     124   3     |
| 13457 8     12345 | 1379  1379  27    | 1245  6     14    |
+-------------------+-------------------+-------------------+

r6c8 = 9 ==> r2c2 = 9 ==> r1c4 or r1c5 = 9 ==> no way to fit a "9" in top right 3x3 box.

Interestingly, there are two strongly linked chains in the "9"s -- you can make the "fork" argument using row 3 and column 2. You can also use the same technique to eliminate a "2" at r8c3 (via row 1 and column 7) and a "5" at r6c2 (via row 2 and column 6). I don't see how to reduce either of those eliminations to "Nishio," however. dcb
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PostPosted: Sat Apr 08, 2006 1:13 pm    Post subject: Reply with quote

I think one of the biggest objections to Havards origional post was the naming of specific patterns that were merely part of a more general technique that already had a name and his insistence, while aknowledging that they were merely subsets, on using his new names. To many people is was like having a different name for every possible variation of, for example, a finned swordfish.

I do know that many people replied to his post (here) saying that it was a very clear explanation of the logic behind conjugate links and colouring, for which they were grateful, as some of the other things they had read were not nearly so clear and well explained.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sat Apr 08, 2006 1:15 pm    Post subject: Reply with quote

The above post is mine, but forgot to log in.
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