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What is this called

 
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George Woods



Joined: 28 Mar 2006
Posts: 234
Location: Dorset UK

PostPosted: Mon Aug 20, 2007 2:23 pm    Post subject: What is this called Reply with quote

The following puzzle came from the telegraph and was graded as too Hard
This is the state after standard moves
Code:

+-------+-------+-------+
| 5 1 . | 3 2 . | 4 9 . |
| . . . | . 5 4 | . 1 3 |
| 3 . 4 | 6 1 9 | 5 . 2 |
+-------+-------+-------+
| 8 . 5 | 2 . . | 1 . 9 |
| . 6 . | 1 9 5 | . 4 . |
| 9 . 1 | . . . | 2 . 5 |
+-------+-------+-------+
| 1 . . | 5 7 . | . . 4 |
| 4 5 . | 9 8 . | . . 1 |
| . 2 . | 4 . 1 | . 5 . |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site

Before solving it with a forcing chaim I noticed that a 6 at r9c9 is disastrous, in that there is no place for a 6 allowed in box 7, Since draw/play could not find this it can't be too obvious yet it is fairly easy to spot- so what is this elimination called?

If this is the wrong section to contribute this I will delete it if advised!
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TKiel



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

PostPosted: Mon Aug 20, 2007 3:13 pm    Post subject: Reply with quote

This is known by many names. I call it multi-coloring, since it involves more that one strongly linked chain. The chains are connected by a weak link.

In this configuration, it would exclude the <6> from r9c9.

Code:

 *--------------------------------------------------------------------*
 |               678B   |                      |               678b   |
 | 267A          26789  |                      | 678                  |
 |                      |                      |                      |
 |----------------------+----------------------+----------------------|
 |                      |        346    367    |        367           |
 |                      |                      |                      |
 |                      |        346    3678   |        367           |
 |----------------------+----------------------+----------------------|
 |               3689   |               236    | 3689                 |
 |               367    |               236    | 367                  |
 | 67a           36789  |        36            | 36789        -678    |
 *--------------------------------------------------------------------*


In this configuration, it would exclude the <6> from r1c3 & r2c7.

Code:

 *--------------------------------------------------------------------*
 |              -678    |                      |               678b   |
 | 267a          26789  |                      |-678                  |
 |                      |                      |                      |
 |----------------------+----------------------+----------------------|
 |                      |        346    367    |        367           |
 |                      |                      |                      |
 |                      |        346    3678   |        367           |
 |----------------------+----------------------+----------------------|
 |               3689   |               236    | 3689                 |
 |               367    |               236    | 367                  |
 | 67A           36789  |        36            | 36789         67B    |
 *--------------------------------------------------------------------*


I would configure it like this, which would place the <6> in r1c9, effectively accomplishing both steps above in one move.

Code:

 *--------------------------------------------------------------------*
 |               678B   |                      |               678b   |
 | 267a          26789  |                      | 678B                  |
 |                      |                      |                      |
 |----------------------+----------------------+----------------------|
 |                      |        346    367    |        367           |
 |                      |                      |                      |
 |                      |        346    3678   |        367           |
 |----------------------+----------------------+----------------------|
 |               3689   |               236    | 3689                 |
 |               367    |               236    | 367                  |
 | 67A           36789  |        36            | 36789         67B    |
 *--------------------------------------------------------------------*


Others may call it fork, color wing, two-string kite (aaaaaaah!), skyscraper (aaaaaaah!), turbot fish, etc.
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Marty R.



Joined: 12 Feb 2006
Posts: 5165
Location: Rochester, NY, USA

PostPosted: Mon Aug 20, 2007 3:54 pm    Post subject: Reply with quote

Tracy, your first two examples are pretty conventional strong links but I don't have a clue about the third, with three capital "Bs" and one lower case, with that r2c7 seemingly sitting in limbo.
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TKiel



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

PostPosted: Mon Aug 20, 2007 4:19 pm    Post subject: Reply with quote

The third example shows B as a peer of both A & a, which means that b must be where the digit is.
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Tue Aug 21, 2007 11:13 pm    Post subject: Reply with quote

Actually, I like Havard's descriptions of "skyscraper" and "2 string kite". For the visual amongst us they are very allegorical and work well.
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