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Come Fly With Me

 
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keith



Joined: 19 Sep 2005
Posts: 3331
Location: near Detroit, Michigan, USA

PostPosted: Wed May 16, 2018 11:48 am    Post subject: Come Fly With Me Reply with quote

A nice example, found in a booklet of puzzles from the dollar store. They say: kappapuzzles.com
Code:
Puzzle: Fly With Me
+-------+-------+-------+
| . . . | 7 . . | 5 . . |
| . . . | 5 . 2 | . . 9 |
| . 9 2 | . 4 . | . 8 . |
+-------+-------+-------+
| 3 4 . | . 9 . | . 5 . |
| . . 1 | . . . | 8 . . |
| . 5 . | . 1 . | . 4 2 |
+-------+-------+-------+
| . 7 . | . 5 . | 2 1 . |
| 9 . . | 1 . 4 | . . . |
| . . 4 | . . 6 | . . . |
+-------+-------+-------+

Keith
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ZeroAssoluto



Joined: 05 Feb 2017
Posts: 229
Location: Rimini, Italy

PostPosted: Wed May 16, 2018 1:46 pm    Post subject: Reply with quote

Hi everyone,

Code:

+----------------+-------------+-------------+
| 4    368  368  | 7   368 9   | 5   2   1   |
| 1678 1368 3678 | 5   368 2   | 4   36  9   |
| 5    9    2    | 36  4   1   | 367 8   367 |
+----------------+-------------+-------------+
| 3    4    678  | 2   9   78  | 1   5   67  |
| 267  26   1    | 4   36  5   | 8   9   367 |
| 678  5    9    | 368 1   378 | 367 4   2   |
+----------------+-------------+-------------+
| 68   7    368  | 9   5   38  | 2   1   4   |
| 9    23   5    | 1   27  4   | 36  367 8   |
| 128  1238 4    | 38  27  6   | 9   37  5   |
+----------------+-------------+-------------+

Play this puzzle online at the Daily Sudoku site

W-Wing 3,6 in r3c4,r5c5 connected by number 3 in r35c9 and -6 in r12c5,r6c4.

Ciao Gianni
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keith



Joined: 19 Sep 2005
Posts: 3331
Location: near Detroit, Michigan, USA

PostPosted: Wed May 16, 2018 4:00 pm    Post subject: Reply with quote

Actually, I was thinking of the M-wing:
Code:
+----------------+----------------+----------------+
| 4    368  368  | 7    368  9    | 5    2    1    |
| 1678 1368 3678 | 5    368  2    | 4    36   9    |
| 5    9    2    | 36a  4    1    | 367  8   -367  |
+----------------+----------------+----------------+
| 3    4    678  | 2    9    78   | 1    5    67   |
| 267  26   1    | 4    36b  5    | 8    9    367c |
| 678  5    9    | 368  1    378  | 367  4    2    |
+----------------+----------------+----------------+
| 68   7    368  | 9    5    38   | 2    1    4    |
| 9    23   5    | 1    27   4    | 36   367  8    |
| 128  1238 4    | 38   27   6    | 9    37   5    |
+----------------+----------------+----------------+

a and b are the same in the solution; a and c are pincers on 3, eliminated in R3C9.

Keith


Last edited by keith on Fri May 18, 2018 4:25 am; edited 2 times in total
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immpy



Joined: 06 May 2017
Posts: 148

PostPosted: Fri May 18, 2018 3:23 am    Post subject: Reply with quote

Indeed, I was able to spot and utilize the W-Wing. At present, I don't have the skill with M-Wings. Will need to become more familiar and comfortable with the technique.
Thanks for posting the puzzle, Keith.

cheers...immp
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immpy



Joined: 06 May 2017
Posts: 148

PostPosted: Fri May 18, 2018 4:35 am    Post subject: Reply with quote

WooHoo!!!

I think I got it! Just got done reading up on the M-Wing in an earlier thread topic from Keith. And I see it quite clearly now. This is GOOD STUFF! I have learned something new today.
Here is the link to the earlier thread
http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2143

cheers...immp
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keith



Joined: 19 Sep 2005
Posts: 3331
Location: near Detroit, Michigan, USA

PostPosted: Sat May 19, 2018 3:45 am    Post subject: Reply with quote

immpy wrote:
WooHoo!!!

I think I got it! Just got done reading up on the M-Wing in an earlier thread topic from Keith. And I see it quite clearly now. This is GOOD STUFF! I have learned something new today.
Here is the link to the earlier thread
http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2143

cheers...immp

The M-wing and W-wing are first cousins.

The M-wing idea is this: Suppose I have two cells that do not "see" each other, and each has the possibilities XY. What can you do?

Well, suppose you can prove they are the same: If one is X, the other must be X. Then, suppose one of them is an end of a strong link in Y. Now you have found pincers on Y.

X, Y: Unsolved digits
a, b: Any other digits
= : Single digit strong link
- : Link

XY - - XY = aY

is an M-wing with pincers on Y, if you can prove the two XY cells have the same value in the solution.

Nataraj and Asellus generalized this to what was called a half-wing:

XY -- bXY = aY

This is a half wing because it is not symmetric. If the first cell is X, the cell bXY is also X. But, you cannot say, if the bXY cell is X, the first cell is also X.

re'born then came along and observed that M-wings are often a cycle: The pincers lie in the same house. In a cyclic XY-chain, all the links become strong and further eliminations are available.

This is the progression of the discussion you will see in the thread posted by immpy above.

(You may have no idea what this means: In a cyclic XY-chain, all the links become strong ... It does not much matter.)

Keith
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