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16 x 16 broken?

Submitted by: barclay

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Another day, another puzzle to solve.
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9:09 Dog day fireworks?? Maen
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Great fireworks, a reminder to celebrate something this weekend.
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almost a 4 for 4 on dogs. Sooo close.
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Good Maen to all! I think you might have been right Fred!! Looks like a dog shaking off water after a bath!
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Easy today.

1/ Easy up to 42. At this point we have:

a/ locked triplet c1=12, c2=27, c3=17
d/f5=59, f3=569
e/ b9=25, b8=245, b3=4569,b2=56, b1=569

2/ b9=5 => b2=6, b1=9, f3=9, f5=5 and f2=6 . So b9=2, otherwise b9=5 and b2=f2=6. UP to 81.
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I didn't see Sergio's proof before I did mine, but it is very similar:

1) Start 23, Unique Possibilities to (UP) 27.
2) Locked 9s at hi6 forbid ade6=9. UP 42.
3) Locked 6s at d89 forbid d1=6.
4) a789=5 == a3=5 -- i3=5 == i3=6 -- f3=6 == f2=6 -- f2=5 == b2=5 forbids b89=5. UP 81.

This chain comes from finding that b9=5 forces f3=6 and i3=6.
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Another solution to 'tough' sudoku of 08 26 06:

1) Start at 23 filled - the given puzzle. Unique Possibilities to 27 filled. (UP 27).
2) Locked 9's at hi6 forbids ade6=9. UP 42
3a) Locked 1's at a79 forbids a3=1
3b) Locked 2's at b89 forbids b12=2
3c) Locked 7's at c23 More...
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Nice proof Clark. It is a bit better then mine. There is a depth 3 solution possible also:
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Yet another solution to 'tough' sudoku of 08 26 06: (borrowing an idea from Clark, Sergio)

1) Start at 23 filled - the given puzzle. Unique Possibilities to 27 filled. (UP 27).
2) Locked 9's at hi6 forbids ade6=9. UP 42
3a) Locked 2's at b89 forbids b12=2
3b) b2=5 == b2=6 -- More...
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Thanks for the comments on yesterdays tough. Is that step not valid because for a weak link, both sides can't be true? Only 1 of them can be true?
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Forgot to sign again. The fireworks were at 'Kaboom' in San Francisco...the photo doesn't do them justice.

This tough took me one guess.

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to Steve: reading some old forums I found something called the 'extended subset principle' and the
'Sue de Coq'. Given how often one finds naked sets, you'd think they would be quite frequent - are they worth looking for? (seems that ALS is a specialization of the extended subset principle)
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fairly simple one today
have a great day/night one and all
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I moved so I could see more fireworks for free
Montclair State Univ.
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4th of July?
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Sergio, do consider classifying your solution as 'sudoku technique' rather than 'general'. I'd have missed it had Clarke not made reference to your solution, as most days I only check the box for the techniques. It's a pity to miss seeing someone's solution for this reason. Am I the only one who doesn't read the 'general' comments?
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9:15 after setup. Pretty easy today. Happy weekend, all!
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Hi pat!
Extended subsets are not that frequent, neither is the 'Sue De Coq'. I have used both before, but have not named them as such(they also may not have made it past the cutting table.) Both are just an extension of the ALS idea, and also are well expressed as pigeonhole matrices. There are More...
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Hi Jeff!
You had something like:
cellx=ab -- celly=ab
Care must be exercised when using compound arguments in a chain. Although cellx=a -- celly=a is clear - and generally just a native weak link - what does it really mean?
It means: cellx=a is false OR cellx=b is false.
We say in More...
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BTW - it is interesting that those in the forum though enough of Sue to name a technique after her.
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Keyan: I have enjoyed your pictures. Thanks
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hehe - him...
17/Apr/07 6:45 PM
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Sept. 29, 2007.
29/Sep/07 9:53 PM
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vrswz fqdnghuw jnpuqvabi khnqa zgshrt wcrkj ctlywhx
02/Oct/07 2:27 AM
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bfuk sulfij tasze egtr bicp izxtoqe ingkma http://www.mndzeo.oeuynixp.com
02/Oct/07 2:27 AM
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05/Sep/10 9:39 PM
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