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Captain Pete
Joined: 09 Jun 2007
Posts: 55
Location: Oley, PA
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 Posted: Fri Feb 08, 2008 2:22 pm Post subject: Very easy, but stuck |
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An easy newspaper puzzle this week has me stumped. I solved the puzzle very quickly without pencil marks. My wife got the puzzle to this point, and got stuck. I attempted to finish it for her, but couldn't see an easy key to the puzzle. Keep in mind, this is a two-star easy puzzle, so shouldn't require advanced techniques. What is the next step?
[code]
+--------+----------+----------+
| 4 9 8 | 7 2 35 | 35 1 6 |
| 6 7 5 | 1 89 38 | 389 2 4 |
| 3 2 1 | 6 589 4 | 589 58 7 |
+--------+----------+----------+
| 58 3 9 | 4 7 1 | 6 58 2 |
| 7 1 6 | 2 58 58 | 4 3 9 |
| 58 4 2 | 3 6 9 | 58 7 1 |
+--------+----------+----------+
| 2 6 4 | 8 3 7 | 1 9 5 |
| 9 8 7 | 5 1 6 | 2 4 3 |
| 1 5 3 | 9 4 2 | 7 6 8 |
+--------+----------+----------+ |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Fri Feb 08, 2008 4:30 pm Post subject: |
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I re-post the grid for better readability:
| Code: |
+--------------------------+--------------------------+--------------------------+
| 4 9 8 | 7 2 35 | 35 1 6 |
| 6 7 5 | 1 89 38 | 389 2 4 |
| 3 2 1 | 6 589 4 | 589 58 7 |
+--------------------------+--------------------------+--------------------------+
| 58 3 9 | 4 7 1 | 6 58 2 |
| 7 1 6 | 2 58 58 | 4 3 9 |
| 58 4 2 | 3 6 9 | 58 7 1 |
+--------------------------+--------------------------+--------------------------+
| 2 6 4 | 8 3 7 | 1 9 5 |
| 9 8 7 | 5 1 6 | 2 4 3 |
| 1 5 3 | 9 4 2 | 7 6 8 |
+--------------------------+--------------------------+--------------------------+
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This BUG+3 can be solved by noting that in order to avoid the deadly pattern, either
r2c7=8 or r3c5=8 or r3c7=5 (the extra numbers in both row and column)
In every case I get r1c6=5.
Shortly after, there is a UR 89 which makes r3c7=5. This solves the puzzle.
Not basics steps at all....   |
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Fri Feb 08, 2008 4:37 pm Post subject: |
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The puzzle has four solutions. Your wife has reached the most complete grid common to all four so the next step is a guess.
Could a clue have been missed when transcribing it?
Steve |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Fri Feb 08, 2008 4:41 pm Post subject: |
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Ah, zut!
And I drew conclusions from the assumption that there was a unique solution ...
ex falso quodlibet
Well - found at least one of those 4 solutions ... |
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Fri Feb 08, 2008 5:27 pm Post subject: |
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Yes, your method seemed to work very well.
Maybe paraconsistent logic is more useful than I thought!
Steve |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Feb 08, 2008 5:55 pm Post subject: |
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| Quote: | | ex falso quodlibet |
Q: How many dictionaries does it take to understand a Sudoku forum?
A: Indeterminate  |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Fri Feb 08, 2008 6:07 pm Post subject: |
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That's a good one, Marty,
| Marty R. wrote: |
Q: How many dictionaries does it take to understand a Sudoku forum?
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Probably just mathematics and logic
But I admit, that "zut" is no expression from mathematics. It should probably be in the French (slang?) dictionary. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Fri Feb 08, 2008 7:04 pm Post subject: |
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This one you can solve manually without guessing. You just have to distinguish 2 cases.
| Code: | +--------------------------+--------------------------+--------------------------+
| 4 9 8 | 7 2 35 | 35 1 6 |
| 6 7 5 | 1 9 38 | 38 2 4 |
| 3 2 1 | 6 58 4 |#589 #58 7 |
+--------------------------+--------------------------+--------------------------+
|#58 3 9 | 4 7 1 | 6 #58 2 |
| 7 1 6 | 2 58 58 | 4 3 9 |
|#58 4 2 | 3 6 9 |#58 7 1 |
+--------------------------+--------------------------+--------------------------+
| 2 6 4 | 8 3 7 | 1 9 5 |
| 9 8 7 | 5 1 6 | 2 4 3 |
| 1 5 3 | 9 4 2 | 7 6 8 |
+--------------------------+--------------------------+--------------------------+
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The marked cells form a deadly pattern for 58. In a unique puzzle this would mean r3c7=9:
| Code: | +--------------------------+--------------------------+--------------------------+
| 4 9 8 | 7 2 35 | 35 1 6 |
| 6 7 5 | 1 9 38 | 38 2 4 |
| 3 2 1 | 6 58 4 | 9 58 7 |
+--------------------------+--------------------------+--------------------------+
| 58 3 9 | 4 7 1 | 6 58 2 |
| 7 1 6 | 2 58 58 | 4 3 9 |
| 58 4 2 | 3 6 9 | 58 7 1 |
+--------------------------+--------------------------+--------------------------+
| 2 6 4 | 8 3 7 | 1 9 5 |
| 9 8 7 | 5 1 6 | 2 4 3 |
| 1 5 3 | 9 4 2 | 7 6 8 |
+--------------------------+--------------------------+--------------------------+
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This immediately gives 2 solutions, r2c6=8 and r1c6=5 fix all cells (both the 58-chain and the block with 3's). In fact its just a more difficult deadly pattern.
Now what if r3c7<>9 ? Then r3c5=9, r2c7=9 etc. and all cells but the DP are fixed.
| Code: | +--------------------------+--------------------------+--------------------------+
| 4 9 8 | 7 2 5 | 3 1 6 |
| 6 7 5 | 1 8 3 | 9 2 4 |
| 3 2 1 | 6 9 4 | 58 58 7 |
+--------------------------+--------------------------+--------------------------+
| 58 3 9 | 4 7 1 | 6 58 2 |
| 7 1 6 | 2 5 8 | 4 3 9 |
| 58 4 2 | 3 6 9 | 58 7 1 |
+--------------------------+--------------------------+--------------------------+
| 2 6 4 | 8 3 7 | 1 9 5 |
| 9 8 7 | 5 1 6 | 2 4 3 |
| 1 5 3 | 9 4 2 | 7 6 8 |
+--------------------------+--------------------------+--------------------------+
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So you have two more solutions with the deadly pattern left.
[Added:]Multisolution puzzles are a kind of sudoku variant (invented by me  ), where you can learn about deadly patterns. This is a very easy one:
| Code: | 1 . . . . . . . 2
. . . 3 . 4 . . .
. . 4 . . . 5 . .
. 4 . . . . . 6 .
7 . . . 2 . . . 8
. 3 . . . . . 4 .
. . 1 . . . 3 . .
. . . 7 . 5 . . .
9 . . . . . . . 1 JPF
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Feb 08, 2008 9:30 pm Post subject: |
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Pete,
Can you post the original puzzle?
Nataraj,
| Quote: | | And I drew conclusions from the assumption that there was a unique solution ... |
Which, in my mind, is not a problem. You have assumed there is one solution, and you have found one solution.
If you had set out to prove there is only one solution, that is a different matter.
Keith |
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