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KITE

 
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CORUJA



Joined: 16 Jun 2007
Posts: 14
Location: BRUMADINHO - MG; BRAZIL

PostPosted: Sun Apr 27, 2008 12:39 pm    Post subject: KITE Reply with quote

Could someone of the Sudoku Masters explain what a "kite" is and how it works?
Thanks,
Coruja
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Marty R.



Joined: 12 Feb 2006
Posts: 5153
Location: Rochester, NY, USA

PostPosted: Sun Apr 27, 2008 3:58 pm    Post subject: Reply with quote

Coruja,

This is an outline of a kite from Havard's post about strong links. The concept of a kite is the same as a skyscraper, but the strong links aren't parallel, they both originate from the same box and go out at right angles.

Code:
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
. . A----------B . .
. . . | . . . | . . .
. C . | . . . | . . .
--|---+-------+------
. | . | . . . | . . .
. D . | . . . | * . .
. . . | . . . | . . .

Since AB and CD are both strong links on the same number, any cell that sees both B and D can have that number eliminated.

The full post is here:

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



Joined: 03 Aug 2007
Posts: 1029
Location: Vienna, Austria

PostPosted: Sun Apr 27, 2008 5:45 pm    Post subject: Examples Reply with quote

Kite (and skyscraper) example: April 21 VH (see this thread)

The position:
Code:

+--------------------------+--------------------------+--------------------------+
| 1       57      458      | 38      348     2        | 6       9       78       |
| 27      6       48       | 9       48      5        | 3       1       27       |
| 28      3       9        | 16      7       16       | 48      45      258      |
+--------------------------+--------------------------+--------------------------+
| 3       8       6        | 7       1       4        | 5       2       9        |
| 5       2       1        | 368     9       368      | 47      47      68       |
| 9       4       7        | 5       2       68       | 18      3       168      |
+--------------------------+--------------------------+--------------------------+
| 4       157     58       | 138     6       9        | 2       57      135      |
| 6       9       2        | 4       35      137      | 17      8       135      |
| 78      157     3        | 2       58      178      | 9       6       4        |
+--------------------------+--------------------------+--------------------------+

contains many cells with candidate "8":
Code:
            
+-------+-------+-------+   
| . . 8 | 8 8 . | . . 8 |   
| . . 8 | . 8 . | . . . |   
| 8 . . | . . . | 8 . 8 |   
+-------+-------+-------+   
| . . . | . . . | . . . |   
| . . . | 8 . 8 | . . 8 |   
| . . . | . . 8 | 8 . 8 |   
+-------+-------+-------+   
| . . 8 | 8 . . | . . . |   
| . . . | . . . | . . . |   
| 8 . . | . 8 8 | . . . |
+-------+-------+-------+

Look at those rows and colums where 8 occurs exactly twice.
The two cells in such a row or column form a so called "strong link" (strong link means: if one cell is NOT 8, then the other must be 8. There are other possibilities for strong links, but the most common by far is a candidate in only two cells in a row or column or box)

Such "strong links" exist in row 2, row 7, col 1 and col 7. There is also box 7

I've left out all the other positions and drawn only the strong links here:
Code:
            
+-------+-------+-------+   
| . . . | . . . | . . . |   
| . . *-----* . | . . . |   
| * . . | . . . | * . . |   
+-|-----+-------+-|-----+   
| | . . | . . . | | . . |   
| | . . | . . . | | . . |   
| | . . | . . . | * . . |   
+-|-----+-------+-------+   
| | . *---* . . | . . . |   
| | / . | . . . | . . . |   
| * . . | . . . | . . . |
+-------+-------+-------+


Rows 2 and 7 form a "skyscraper". The strong links are parallel (rows 2,7) and they share a common column (col 2). Any cell that "sees" the two ends (r2c5, r7c4) cannot contain "8"

Code:
            
+-------+-------+-------+   
| . . . | X . . | . . . |   
| . . *===X=* . | . . . |   
| * . . | X . . | * . . |   
+-|-----+-------+-|-----+   
| | . . | . . . | | . . |   
| | . . | . . . | | . . |   
| | . . | . . . | * . . |   
+-|-----+-------+-------+   
| | . *===* X . | . . . |   
| | / . | . X . | . . . |   
| * . . | . X . | . . . |
+-------+-------+-------+


There is another skyscraper in cols 1 and 7

Code:

+-------+-------+-------+   
| . . . | . . . | . . . |   
| . . *-----* . | . . . |   
| * . . | . . . | * . . |   
+-"-----+-------+-"-----+   
| " . . | . . . | " . . |   
| " . . | . . . | " . . |   
| " . . | . . . | * . . |   
+-"-----+-------+-------+   
| " . *---* . . | . . . |   
| " / . | . . . | . . . |   
| * . . | . . . | . . . |
+-------+-------+-------+

There are no eliminations that can be made using this skyscraper.

Where are the kites?

One is formed by the strong links in col 1 and row 2:
Code:

+-------+-------+-------+   
| . . . | . . . | . . . |   
| . . *=====* . | . . . |   
| * . . | . . . | * . . |   
+-"-----+-------+-|-----+   
| " . . | . . . | | . . |   
| " . . | . . . | | . . |   
| " . . | . . . | * . . |   
+-"-----+-------+-------+   
| " . *---* . . | . . . |   
| " / . | . . . | . . . |   
| * . . | . X. | . . . |
+-------+-------+-------+

Cell r9c5 cannot contain 8.

And another kite in col 1 and row 7:
Code:

+-------+-------+-------+   
| . . . | . . . | . . . |   
| . . *-----* . | . . . |   
| * . . | X . . | * . . |   
+-"-----+-------+-|-----+   
| " . . | . . . | | . . |   
| " . . | . . . | | . . |   
| " . . | . . . | * . . |   
+-"-----+-------+-------+   
| " . *===* . . | . . . |   
| " / . | . . . | . . . |   
| * . . | . . . | . . . |
+-------+-------+-------+


r3c4 cannot contain 8.
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