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bernard
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 Posted: Wed Jan 25, 2006 9:20 am Post subject: jan 24 puzzle |
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| hi, i m stuck after 25 moves. who can help ? |
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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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| Posted: Wed Jan 25, 2006 12:24 pm Post subject: I need more information ... |
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Hi, Bernard!
I can probably help you. But I need to know exactly where you got stuck. There are a whole lot of different ways to make 25 moves on a sudoku!
Please post your position. dcb |
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bernard
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| Posted: Wed Jan 25, 2006 4:03 pm Post subject: my position |
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9.5 .76 4..
3.6 ... 597
.47 ..9 ..6
572 6.8 .41
16. .47 ..5
4.. 1.5 67.
65. 7.3 124
731 ... 869
..4 .61 753
thank u for help |
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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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| Posted: Wed Jan 25, 2006 7:34 pm Post subject: This is a "Nightmare", Bernard |
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Hi again, Bernard. I got confused because you were talking about one of Ruud's "Nightmare" puzzles -- I thought you were asking about a puzzle from Samgj's Daily Sudoku site!
Anyway, at the point you've reached the matrix of possibilities looks like this.
| Code: | 9 128 5 238 7 6 4 138 28
3 128 6 248 128 24 5 9 7
28 4 7 2358 12358 9 23 138 6
5 7 2 6 39 8 39 4 1
1 6 389 239 4 7 239 38 5
4 89 389 1 239 5 6 7 28
6 5 89 7 89 3 1 2 4
7 3 1 245 25 24 8 6 9
28 289 4 89 6 1 7 5 3 |
Let's concentrate on r7c5, where the {8, 9} pair is possible. And let's assume that r7c5 = 9. We derive a contradiction pretty quickly, as follows.
r7c5 = 9 ==> r7c3 = 8 ==> {3, 9} pair in r5c3 & r6c3
r7c5 = 9 ==> r4c5 = 3 ==> r6c5 = 2 ==> r6c9 = 8 ==> r6c2 = 9
But now we've reached a contradiction, because there's no way to fit an "8" in the center left 3x3 box. So r7c5 <> 9, and we must have r7c5 = 8. With this one additional value set you should be able to complete the puzzle. dcb
PS In an earlier post I said there were two closely related forcing chains in the puzzle, but I was wrong -- this one chain at r7c5 is enough to do the trick. |
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bernard
Joined: 25 Jan 2006
Posts: 1
Location: france
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| Posted: Thu Jan 26, 2006 2:45 pm Post subject: |
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 thank u for this chain I hadn't found
________
Ford Fiesta RS Turbo specifications
Last edited by bernard on Mon Jan 31, 2011 6:34 pm; edited 1 time in total |
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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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| Posted: Thu Jan 26, 2006 5:19 pm Post subject: There's another to view the same formation |
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You're welcome, Bernard.
Looking at this again, I notice another way of viewing it that may seem more intuitive ...
| Code: | 9 128 5 238 7 6 4 138 28
3 128 6 248 128 24 5 9 7
28 4 7 2358 12358 9 23 138 6
5 7 2 6 39 8 39 4 1
1 6 389 239 4 7 239 38 5
4 89 389 1 239 5 6 7 28
6 5 89 7 89 3 1 2 4
7 3 1 245 25 24 8 6 9
28 289 4 89 6 1 7 5 3 |
Think about what will happen if r6c2 = 8. This will change the {3, 8, 9} in r5c3 & r6c3 into a {3, 9} pair, forcing an "8" at r7c3.
But r6c2 = 8 also forces r6c9 = 2, which creates the {3, 9} pair in r4c5 & r6c5, forcing an "8" at r7c5. But we can't have two "8"s in row 7, so r6c2 = 9.
It's a cute pattern. dcb |
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