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Marty R.
Joined: 12 Feb 2006 Posts: 5770 Location: Rochester, NY, USA
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Posted: Wed Aug 25, 2010 1:52 am Post subject: Is this a valid kite? |
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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 |
+-----------------+-------------+------------+
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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: 2468 Location: Northern California Foothills
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Posted: Wed Aug 25, 2010 2:15 am Post subject: |
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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: 5770 Location: Rochester, NY, USA
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Posted: Wed Aug 25, 2010 3:46 am Post subject: |
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Thanks Ted, you're very diplomatic. It wasn't a typo, just screwed-up logic, or lack of same. |
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Marty R.
Joined: 12 Feb 2006 Posts: 5770 Location: Rochester, NY, USA
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Posted: Wed Aug 25, 2010 4:20 am Post subject: |
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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: 3355 Location: near Detroit, Michigan, USA
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Posted: Wed Aug 25, 2010 5:44 am Post subject: |
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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: 2468 Location: Northern California Foothills
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Posted: Wed Aug 25, 2010 2:20 pm Post subject: |
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My phraseology is definitely the greatest; sorry.
Ted |
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daj95376
Joined: 23 Aug 2008 Posts: 3854
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Posted: Wed Aug 25, 2010 3:38 pm Post subject: |
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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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