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crunched
Joined: 05 Feb 2008
Posts: 168
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 Posted: Tue Sep 23, 2008 5:47 am Post subject: Sept 23 VH |
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Wow, this one was really easy. I finished in 8' 17", and I was not trying to be quick. An xy was readily found, and boom it was done. I went back and ran it again, and found an xyz that resolved it.
You masters in this forum will no doubt solve this puzzle in about 45 seconds! |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Tue Sep 23, 2008 11:12 am Post subject: |
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| Quote: | | You masters in this forum will no doubt solve this puzzle in about 45 seconds! |
Yeah: I done it in 44. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Sep 23, 2008 3:42 pm Post subject: |
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Alternate solution. After basics:
| Code: |
+--------+------------+------------+
| 3 4 9 | 6 2 8 | 57 1 57 |
| 5 7 8 | 9 3 1 | 2 4 6 |
| 6 1 2 | 57 4 57 | 3 9 8 |
+--------+------------+------------+
| 9 8 5 | 3 17 2 | 17 6 4 |
| 1 6 3 | 458 78 45 | 9 25 257 |
| 7 2 4 | 15 6 9 | 8 3 15 |
+--------+------------+------------+
| 2 5 1 | 47 9 47 | 6 8 3 |
| 48 9 6 | 1248 5 3 | 14 7 12 |
| 48 3 7 | 1248 18 6 | 145 25 9 |
+--------+------------+------------+
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Play this puzzle online at the Daily Sudoku site
Note in boxes 258, columns 46, the potential DP of 57-57-45-45-47-47. Only an 8 in r5c4 kills it and that solves the puzzle. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Tue Sep 23, 2008 4:05 pm Post subject: |
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Yes, another obvious one-step solution. Not much challenge or fun.
Ted  |
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Clement
Joined: 24 Apr 2006
Posts: 1111
Location: Dar es Salaam Tanzania
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| Posted: Tue Sep 23, 2008 6:05 pm Post subject: |
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| XY-Wing 125 with Pivot{1,2}r8c9 eliminating 5 in r5c8. |
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crunched
Joined: 05 Feb 2008
Posts: 168
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| Posted: Tue Sep 23, 2008 11:03 pm Post subject: |
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| Clement wrote: | | XY-Wing 125 with Pivot{1,2}r8c9 eliminating 5 in r5c8. |
Yes, the 12-25-15 xy-wing eliminates a 5 in r5c8 (pivot on the 12);
or
The 12-25-15 xy-wing eliminates a 2 in r9c8 (pivot on the 15).
and then,
A 257 xyz wing (see boxes 3 & 6) takes out a 5 in r6c9
But I don't quite understand the alternate solution offered by Keith. I guess you are saying that those three sets of double pairs are illegal. Therefore an 8 goes in the box containing 458 as possible candidates. Can you elaborate Keith? |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Sep 24, 2008 12:07 am Post subject: |
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| Quote: | | alternate solution offered by Keith. |
That would be Marty. |
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crunched
Joined: 05 Feb 2008
Posts: 168
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| Posted: Wed Sep 24, 2008 12:34 am Post subject: |
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| keith wrote: | | Quote: | | alternate solution offered by Keith. |
That would be Marty. |
Hmmmm. Keith or Marty. The same number of letters does not mean it is the same person? I see. My bad. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Sep 24, 2008 12:37 am Post subject: |
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| Quote: | | But I don't quite understand the alternate solution offered by Keith. I guess you are saying that those three sets of double pairs are illegal. Therefore an 8 goes in the box containing 458 as possible candidates. Can you elaborate Keith? |
Crunched, the principle is the same as URs. In the latter, if you have all four corners with the same pair, you would have two solutions, because you could interchange the numbers. It's the same here:
| Code: |
+-------+---------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | 57 . 57 | . . . |
+-------+---------+-------+
| . . . | . . . | . . . |
| . . . | 45 . 45 | . . . |
| . . . | . . . | . . . |
+-------+---------+-------+
| . . . | 47 . 47 | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+---------+-------+
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Play this puzzle online at the Daily Sudoku site
You could solve this one way, but then you could swap the numbers and still have a valid solution with each row, column and box containing all three numbers. Since we know that the puzzle has a unique solution, neither of the ones with these numbers can be right because it's not the solution the puzzle constructor created. |
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DennyOR
Joined: 12 Sep 2007
Posts: 33
Location: Portland, Oregon
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| Posted: Wed Sep 24, 2008 4:37 am Post subject: |
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I'm sure this has been asked before but I haven't heard the answer:
I don't like the thought of using a technique that requires that I know that a sudoku has a unique solution. How do I know that a particular sudoku puzzle has a unique solution? |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Sep 24, 2008 5:00 am Post subject: |
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| DennyOR wrote: | I'm sure this has been asked before but I haven't heard the answer:
I don't like the thought of using a technique that requires that I know that a sudoku has a unique solution. How do I know that a particular sudoku puzzle has a unique solution? |
It's specifically stated on this site. This is from the FAQs:
Q3. Does a Sudoku have more than one solution?
Properly formed Sudokus (as available from the Daily Sudoku) always have only one solution. In our view, a Sudoku with more than one solution is not properly formed, but of course puzzles from other sources may have multiple answers. |
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Willzzz
Joined: 22 Aug 2008
Posts: 5
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| Posted: Wed Sep 24, 2008 11:29 am Post subject: |
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| It's an interesting question, in a way it makes a puzzle harder if you cannot use DP techniques. However it makes a lot more sense to have a single solution. To truly answer a double solution puzzle you would have to find both solutions, and if you allow that what if some really sloppy puzzle creaters make a puzzle with more than 2 solutions, eek! |
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DennyOR
Joined: 12 Sep 2007
Posts: 33
Location: Portland, Oregon
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| Posted: Wed Sep 24, 2008 6:24 pm Post subject: |
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I don't know anything about how sudokus are created, and how it's verified that they have only one solution. Could you solve a puzzle with mutliple solutions without noticing that there are more than one solutuion? What happens when you use techniques that require a single solution on a puzzle with mutliple solutions?
In theory, I wouldn't mind solving puzzles with multiple solutions, and would consider any single solution as adequately solving the puzzle. Anyway, for now I'm going to continue to be a recalcitrant and not learn or use the techniques that require a single solution. I seem to be able to solve all the very hards without them. |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Wed Sep 24, 2008 10:23 pm Post subject: |
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How many solutions would this have? Sorry, I'm just being flippant. Though while I'm flipping out - what if I took out the 5 - what are the permutations for a blank sudoku?
| Code: |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . 5 . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
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kragzy
Joined: 01 May 2007
Posts: 112
Location: Australia
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| Posted: Wed Sep 24, 2008 11:10 pm Post subject: |
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Q1: many.
Q2: many, many. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Sep 25, 2008 9:02 am Post subject: |
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| DennyOR wrote: | I don't know anything about how sudokus are created, and how it's verified that they have only one solution. Could you solve a puzzle with mutliple solutions without noticing that there are more than one solutuion? What happens when you use techniques that require a single solution on a puzzle with mutliple solutions?
In theory, I wouldn't mind solving puzzles with multiple solutions, and would consider any single solution as adequately solving the puzzle. Anyway, for now I'm going to continue to be a recalcitrant and not learn or use the techniques that require a single solution. I seem to be able to solve all the very hards without them. |
the way I see it is if you take the uniqueness factor out of the definition of a sudoku puzzle, then you are no longer left with a sudoku puzzle.
if you create a sudoku-like puzzle with many solutions, then how can you call it a sudoku puzzle? it no longer is sudoku if it doesn't have but one solution.
solving sudoku-like puzzles with many solutions is another game and should be called something else.
this website does not offer puzzles that require uniqueness based solutions, but have been proven over and over again to contain them. that is the nature of the beast and one of the nicer surprises.
I will never understand the rationale behind the argument that sudoku puzzles should never be assumed to be unique. the first question that pops in my mind is, "why attempt to solve it?" the whole premise on any solution technique IS uniqueness   one of the reasons I got hooked on sudoku in the first place is because there is only one solution and finding it was oh so satisfying. |
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DennyOR
Joined: 12 Sep 2007
Posts: 33
Location: Portland, Oregon
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| Posted: Thu Sep 25, 2008 7:15 pm Post subject: |
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It's interesting that the responders to my last post completely ignored my questions
Since the FAQs state that "In our view, a Sudoku with more than one solution is not properly formed, but of course puzzles from other sources may have multiple answers.", I assume that somebody has devised sudokus with multiple answers. Could someone post a sudoku with multiple answers (and I don't mean with a single 5 in the center) so that I can verify for myself that solving one is different enough from solving a sudoku with only one solution that it can no longer be called a sudoku puzzle. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Sep 25, 2008 10:47 pm Post subject: |
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| DennyOR wrote: | I don't know anything about how sudokus are created, and how it's verified that they have only one solution.
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Puzzles are created a number of ways. Not everyone verifies the uniqueness of their solutions. Thus, tons of discussion over the years! The only way I know to verify that a puzzle has one solution is through a (brute force) backtracking solver.
| Quote: | Could you solve a puzzle with mutliple solutions without noticing that there are more than one solution?
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It's done all the time. People make a guess at an assignment/elimination and proceed to what they think is the solution.
| Quote: | What happens when you use techniques that require a single solution on a puzzle with mutliple solutions?
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There has been tons of discussion on this point. I have joined those who check a puzzle for a unique solution before trying to solve it. Then, the use of uniqueness techniques in the solution is no longer in question.
| Quote: | In theory, I wouldn't mind solving puzzles with multiple solutions, and would consider any single solution as adequately solving the puzzle. Anyway, for now I'm going to continue to be a recalcitrant and not learn or use the techniques that require a single solution. I seem to be able to solve all the very hards without them.
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What constitutes solving a multiple solution puzzle? At some point, the traditional techniques aren't going to work and you will be stuck with a partially solved puzzle. How do you determine the next assignment/elimination?
| Quote: | It's interesting that the responders to my last post completely ignored my questions.
Since the FAQs state that "In our view, a Sudoku with more than one solution is not properly formed, but of course puzzles from other sources may have multiple answers.", I assume that somebody has devised sudokus with multiple answers. Could someone post a sudoku with multiple answers (and I don't mean with a single 5 in the center) so that I can verify for myself that solving one is different enough from solving a sudoku with only one solution that it can no longer be called a sudoku puzzle.
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If you want puzzles with multiple solutions, then go buy one of the many handheld Sudoku games on the market -- especially the cheaper models! |
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DennyOR
Joined: 12 Sep 2007
Posts: 33
Location: Portland, Oregon
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| Posted: Fri Sep 26, 2008 1:14 am Post subject: |
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Thanks, daj, for addressing my questions.
I didn't realize that you have to make a guess to solve any sudoku with multiple solutions, but perhaps that's obvious. I don't really want to do puzzles that require guessing, unless maybe it's at a point where it's obvious that either guess will lead to a different solution. I wouldn't want to be guessing whether I need to make a guess. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Sep 26, 2008 9:54 pm Post subject: |
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| cgordon wrote: | How many solutions would this have? Sorry, I'm just being flippant. Though while I'm flipping out - what if I took out the 5 - what are the permutations for a blank sudoku?
| Code: |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . 5 . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
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The answers are in the Wikipedia article on Sudoku. Or, do a Google search on mathematics of sudoku
To answer part of your question, the grid with one clue has the same number of solutions as a grid with no clues.
A mathematician would say the cell must contain something, and that 5 is interchangeable with any other value. The 5 does not constrain the number of solutions. Neither does this: | Code: |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| 1 2 3 | 4 5 6 | 7 8 9 |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
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We can renumber any Sudoku solution to have this pattern in R5. But this is a constraint: | Code: |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . 5 . | . . . |
| . . . | . . . | 6 . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
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The fact that R5C5 and R6C7 are not the same is information not contained in the previous grids.
My attitude on Unique arguments, or chains, or any other solving technique is this: Use them, or not. I don't care. But, please, don't preach the sermon!
Keith |
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