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CORUJA
Joined: 16 Jun 2007
Posts: 15
Location: BRUMADINHO - MG; BRAZIL
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 Posted: Sun Apr 27, 2008 12:39 pm Post subject: KITE |
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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: 5770
Location: Rochester, NY, USA
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| Posted: Sun Apr 27, 2008 3:58 pm Post subject: |
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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: 1048
Location: near Vienna, Austria
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| Posted: Sun Apr 27, 2008 5:45 pm Post subject: Examples |
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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 |
+--------------------------+--------------------------+--------------------------+
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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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