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Is this a valid kite?

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5161
Location: Rochester, NY, USA

PostPosted: Wed Aug 25, 2010 1:52 am    Post subject: Is this a valid kite? Reply with quote

I don't know if it's valid or I got lucky. At any rate, I never tried something like this. (This is Nataraj's RYO #2).

Code:

+-----------------+-------------+------------+
| 8     459  3    | 7  2    1   | 459  45 6  |
| 2469  7    456  | 36 468  348 | 2459 1  28 |
| 246   24   1    | 5  468  9   | 234  38 7  |
+-----------------+-------------+------------+
| 3     8    457  | 1  57   2   | 6    45 9  |
| 14679 1459 4567 | 36 5679 357 | 2345 38 28 |
| 69    59   2    | 4  5689 358 | 35   7  1  |
+-----------------+-------------+------------+
| 5     3    9    | 8  1    6   | 7    2  4  |
| 47    6    8    | 2  457  457 | 1    9  3  |
| 12    12   47   | 9  3    47  | 8    6  5  |
+-----------------+-------------+------------+

Play this puzzle online at the Daily Sudoku site

If r2c9=2, then r5c9=2. If r3c7=2, then r3c12<>2 and r2c1=2. Are r2c1 and r5c9 valid pincers of 2?
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Wed Aug 25, 2010 2:15 am    Post subject: Reply with quote

Marty,

First, I believe you have a typo in your first statement: If r2c9=2, then r5c9=2. It should be If r2c9=2, then r5c9<>2

My understanding of a kite is based on the condition that the cells in the pivot box are false whereas your statement is based on the condition that the hinge cells are true. Using your example,
If r9c2=2 then r3c7<>2, then r3c12=2, not r2c1
If r3c7=2 thenr2c9<>2, then r5c9=2
If r2c7=2 then both r3c7 & r2c9<>2, then r3c12=2 and r5c9=2

Ted
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Marty R.



Joined: 12 Feb 2006
Posts: 5161
Location: Rochester, NY, USA

PostPosted: Wed Aug 25, 2010 3:46 am    Post subject: Reply with quote

Thanks Ted, you're very diplomatic. It wasn't a typo, just screwed-up logic, or lack of same. Embarassed
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Marty R.



Joined: 12 Feb 2006
Posts: 5161
Location: Rochester, NY, USA

PostPosted: Wed Aug 25, 2010 4:20 am    Post subject: Reply with quote

Quote:
My understanding of a kite is based on the condition that the cells in the pivot box are false

Ted, I shouldn't get into theory, but I'm trying to remember when multi-coloring was first explained to me. If the premise is that the pivot box cells are false, then what, since they can both be false?

But if they're based on the premise that they're true, then we have action, since they both can't be true, then one or the other of the other half of the strong links must be true, thus the pincer situation.
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keith



Joined: 19 Sep 2005
Posts: 3174
Location: near Detroit, Michigan, USA

PostPosted: Wed Aug 25, 2010 5:44 am    Post subject: Reply with quote

Ted,

I don't understand what the terms "hinge" and "pivot" have to do with a kite.


Marty,

Your first statement is false, for it has two cells 2 in C9.


The pattern of unsolved 2 is:
Code:
+-----------+-----------+-----------+
|  .  .  .  |  .  .  .  |  .  .  .  |
|  *  .  .  |  .  .  .  |  *  .  *  |
|  *  *  .  |  .  .  .  |  *  .  .  |
+-----------+-----------+-----------+
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  *  .  *  |
|  .  .  .  |  .  .  .  |  .  .  .  |
+-----------+-----------+-----------+
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  *  *  .  |  .  .  .  |  .  .  .  |
+-----------+-----------+-----------+


Some months ago I wrote that with a pattern like this, no two strong link, single-digit eliminations are possible. There cannot be an X-wing, ER, Kite, Skyscraper, Turbot, ...

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=4120

Keith
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Wed Aug 25, 2010 2:20 pm    Post subject: Reply with quote

My phraseology is definitely the greatest; sorry.

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Aug 25, 2010 3:38 pm    Post subject: Reply with quote

Sudopedia has a great description of a 2-String Kite:

http://www.sudopedia.org/wiki/2-String_Kite

As for me, I think of a Kite as two strong links -- one in a row and one in a column. An endpoint from each strong link must be in the same box. There must also be an empty cell where the row and column intersect.

Code:
 ungrouped 2-String Kite               grouped 2-String Kite
 strong links in:      [r2] and [c3]   strong links in:      [r2] and [c3]
 endpoints common in:  [b1]            endpoints common in:  [b1]
 empty of candidate:   r2c3            empty of candidate:   r2c3
 elimination in:       r8c8            elimination in:       r8c8
 +-----------------------+             +-----------------------+
 | . . X | . . . | . . . |             | . . X | . . . | . . . |
 | X / / | / / / | / X / |             | X X / | / / / | / X / |
 | . . / | . . . | . . . |             | . . X | . . . | . . . |
 |-------+-------+-------|             |-------+-------+-------|
 | . . / | . . . | . . . |             | . . / | . . . | . . . |
 | . . / | . . . | . . . |             | . . / | . . . | . . . |
 | . . / | . . . | . . . |             | . . / | . . . | . . . |
 |-------+-------+-------|             |-------+-------+-------|
 | . . / | . . . | . . . |             | . . / | . . . | . . . |
 | . . X | . . . | . * . |             | . . X | . . . | . * . |
 | . . / | . . . | . . . |             | . . / | . . . | . . . |
 +-----------------------+             +-----------------------+
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