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Jan 07 has 3 solutions

 
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jack02



Joined: 08 Jan 2013
Posts: 5

PostPosted: Tue Jan 08, 2013 1:36 pm    Post subject: Jan 07 has 3 solutions Reply with quote

I get a "unique rectangle" 0f 1/6 based on E3,E7,F7,F3. Removing the 1/6 at E3 (because of E7,F7,F3) leaving the 5 results in a valid solution.
However if you assume either 1 or 6 at E3 this also results in valid solutions.
Anyone cofirm this?
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arkietech



Joined: 31 Jul 2008
Posts: 1686
Location: Northwest Arkansas USA

PostPosted: Tue Jan 08, 2013 2:01 pm    Post subject: Reply with quote

All I needed was basics. Locked cells only.
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jack02



Joined: 08 Jan 2013
Posts: 5

PostPosted: Tue Jan 08, 2013 3:54 pm    Post subject: Reply with quote

OK - but see below 3 solutions...

9 4 1 6 5 8 7 2 3
5 2 8 7 3 9 4 1 6
6 3 7 1 2 4 9 5 8
2 7 3 8 6 1 5 4 9
4 1 5 9 7 3 6 8 2
8 9 6 5 4 2 1 3 7
7 5 4 2 8 6 3 9 1
3 8 9 4 1 7 2 6 5
1 6 2 3 9 5 8 7 4

-or-

9 1 4 6 5 8 7 2 3
5 2 8 7 3 9 4 1 6
6 3 7 1 2 4 9 5 8
2 7 3 8 6 1 5 4 9
4 5 1 9 7 3 6 8 2
8 9 6 5 4 2 1 3 7
7 4 5 2 8 6 3 9 1
3 8 9 4 1 7 2 6 5
1 6 2 3 9 5 8 7 4

-or-

9 1 4 6 5 8 7 2 3
5 2 8 7 3 9 4 1 6
6 3 7 1 2 4 9 5 8
2 7 3 8 6 1 5 4 9
4 5 6 9 7 3 1 8 2
8 9 1 5 4 2 6 3 7
7 4 5 2 8 6 3 9 1
3 8 9 4 1 7 2 6 5
1 6 2 3 9 5 8 7 4
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kuskey



Joined: 10 Dec 2008
Posts: 119
Location: Pembroke, NH

PostPosted: Tue Jan 08, 2013 5:50 pm    Post subject: Jan 7 VH Reply with quote

This puzzle has given me fits!! I started with pen/ink and made a mistake so started over. Wasn't paying close attention, arrived at a solution, but don't remember how (maybe an XY, not sure). Switched to online and solved it using basics only. Haven't been able to duplicate that one at all after several retries. Eventually came across a 467 XY pivot r6c3 yielding r9c1<>6 leading to a solution that I can duplicate at will. As for multiple solutions - haven't found any yet, but never know on this one.
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arkietech



Joined: 31 Jul 2008
Posts: 1686
Location: Northwest Arkansas USA

PostPosted: Tue Jan 08, 2013 6:38 pm    Post subject: Reply with quote

jack02 wrote:
OK - but see below 3 solutions...

9 4 1 6 5 8 7 2 3
5 2 8 7 3 9 4 1 6
6 3 7 1 2 4 9 5 8
2 7 3 8 6 1 5 4 9
4 1 5 9 7 3 6 8 2
8 9 6 5 4 2 1 3 7
7 5 4 2 8 6 3 9 1
3 8 9 4 1 7 2 6 5
1 6 2 3 9 5 8 7 4

-or-

9 1 4 6 5 8 7 2 3
5 2 8 7 3 9 4 1 6
6 3 7 1 2 4 9 5 8
2 7 3 8 6 1 5 4 9
4 5 1 9 7 3 6 8 2
8 9 6 5 4 2 1 3 7
7 4 5 2 8 6 3 9 1
3 8 9 4 1 7 2 6 5
1 6 2 3 9 5 8 7 4

-or-

9 1 4 6 5 8 7 2 3
5 2 8 7 3 9 4 1 6
6 3 7 1 2 4 9 5 8
2 7 3 8 6 1 5 4 9
4 5 6 9 7 3 1 8 2
8 9 1 5 4 2 6 3 7
7 4 5 2 8 6 3 9 1
3 8 9 4 1 7 2 6 5
1 6 2 3 9 5 8 7 4


The puzzle has a given of 1 in r6c3 two of your puzzles have a 6 there.

The third/last answer is vaild
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kuskey



Joined: 10 Dec 2008
Posts: 119
Location: Pembroke, NH

PostPosted: Tue Jan 08, 2013 8:35 pm    Post subject: Jan 7 VH Reply with quote

arkietech, help me sort things out. jack02 listed three solutions and you said the third(last) is valid. You also said you solved using basics only. Is your solution in agreement with his third solution? Whether there is agreement or not, can you indicate, in some way, how basics did it for you?

The online daily solver says my solution using a 467 XY wing is correct. I assume you and jack02 also used that solver and it says your solutions are correct. This suggests a puzzle having multiple solutions. So--just how does the daily solver handle a multi-solution puzzle?

Lastly, what is the definitive word on todays puzzle?
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kuskey



Joined: 10 Dec 2008
Posts: 119
Location: Pembroke, NH

PostPosted: Tue Jan 08, 2013 8:45 pm    Post subject: Jan 7 VH Reply with quote

I forgot an important fact--my solution does not agree with jack02's third solution.
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Marty R.



Joined: 12 Feb 2006
Posts: 5063
Location: Rochester, NY, USA

PostPosted: Tue Jan 08, 2013 10:33 pm    Post subject: Reply with quote

First, 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."

I played it online, needed basics only and got this solution:

Code:

+-------+-------+-------+
| 9 1 4 | 6 5 8 | 7 2 3 |
| 5 2 8 | 7 3 9 | 4 1 6 |
| 6 3 7 | 1 2 4 | 9 5 8 |
+-------+-------+-------+
| 2 7 3 | 8 6 1 | 5 4 9 |
| 4 5 6 | 9 7 3 | 1 8 2 |
| 8 9 1 | 5 4 2 | 6 3 7 |
+-------+-------+-------+
| 7 4 5 | 2 8 6 | 3 9 1 |
| 3 8 9 | 4 1 7 | 2 6 5 |
| 1 6 2 | 3 9 5 | 8 7 4 |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site

It is the 3rd solution shown by jack02.
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arkietech



Joined: 31 Jul 2008
Posts: 1686
Location: Northwest Arkansas USA

PostPosted: Tue Jan 08, 2013 10:44 pm    Post subject: Re: Jan 7 VH Reply with quote

kuskey wrote:
arkietech, help me sort things out. jack02 listed three solutions and you said the third(last) is valid. You also said you solved using basics only. Is your solution in agreement with his third solution? Whether there is agreement or not, can you indicate, in some way, how basics did it for you?

The online daily solver says my solution using a 467 XY wing is correct. I assume you and jack02 also used that solver and it says your solutions are correct. This suggests a puzzle having multiple solutions. So--just how does the daily solver handle a multi-solution puzzle?

Lastly, what is the definitive word on todays puzzle?


A puzzle is determined by the given numbers (clues) in a valid puzzle there is only one solution with the given clues. Change the clue you change the puzzle. In this case to an invalid one with at least two results.

Hope this helps.

The third puzzle has only one solution solved with basic moves.
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jack02



Joined: 08 Jan 2013
Posts: 5

PostPosted: Wed Jan 09, 2013 11:13 am    Post subject: Reply with quote

Looks to me like all three solutions contain all the clues in the correct postitions as well as uniquely contain each number 1-9 in rows, columns and boxes.
I know that is not supposed to happen but here it is.
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Thu Jan 10, 2013 12:34 am    Post subject: Re: Jan 07 has 3 solutions Reply with quote

jack02 wrote:
I get a "unique rectangle" 0f 1/6 based on E3,E7,F7,F3. Removing the 1/6 at E3 (because of E7,F7,F3) leaving the 5 results in a valid solution.
However if you assume either 1 or 6 at E3 this also results in valid solutions.
Anyone cofirm this?

I could not find any scenario that has a 16 UR.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5063
Location: Rochester, NY, USA

PostPosted: Thu Jan 10, 2013 12:56 am    Post subject: Reply with quote

If I bring up the puzzle, immediately click Auto Sweep and only type in the answers that show as one possibility left in a cell, I get the following grid:

Code:

+--------+-----------------+-----------------+
| 9  1 4 | 56   56    568  | 7    2     3    |
| 5  2 8 | 1367 13467 9    | 146  146   46   |
| 6  3 7 | 15   2     1458 | 1489 14589 489  |
+--------+-----------------+-----------------+
| 2  7 3 | 8    146   146  | 5    1469  469  |
| 4  5 6 | 9    17    3    | 18   178   2    |
| 8  9 1 | 567  4567  2    | 46   3     467  |
+--------+-----------------+-----------------+
| 37 4 5 | 2367 8     67   | 369  679   1    |
| 37 8 9 | 4    1367  167  | 2    67    5    |
| 1  6 2 | 357  3579  57   | 3489 4789  4789 |
+--------+-----------------+-----------------+

Play this puzzle online at the Daily Sudoku site
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jack02



Joined: 08 Jan 2013
Posts: 5

PostPosted: Thu Jan 10, 2013 12:02 pm    Post subject: Reply with quote

Keith,
For me puzzel resolved to:
9 14 14 6 5 8 7 2 3
5 2 8 7 3 9 4 1 6
6 3 7 1 2 4 9 5 8
2 7 3 8 6 1 5 4 9
4 15 156 9 7 3 16 8 2
8 9 16 5 4 2 16 3 7
7 45 45 2 8 6 3 9 1
3 8 9 4 1 7 2 6 5
1 6 2 3 9 5 8 7 4

At first I was stymied but the 16 combo at box 4 and 6 looked like a deadly pattern so I eliminated leaving the 5, and from there quickly solved.
However I'd never acually tried the "unique rectangle" strategy before, so I decided to just try plugging in the other two values to test. Both the 1 and the 6 also resolved to valid solutions.
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Marty R.



Joined: 12 Feb 2006
Posts: 5063
Location: Rochester, NY, USA

PostPosted: Thu Jan 10, 2013 4:16 pm    Post subject: Reply with quote

Converting jack02's position to grid style.

Code:

+----------+-------+--------+
| 9 14 14  | 6 5 8 | 7  2 3 |
| 5 2  8   | 7 3 9 | 4  1 6 |
| 6 3  7   | 1 2 4 | 9  5 8 |
+----------+-------+--------+
| 2 7  3   | 8 6 1 | 5  4 9 |
| 4 15 156 | 9 7 3 | 16 8 2 |
| 8 9  16  | 5 4 2 | 16 3 7 |
+----------+-------+--------+
| 7 45 45  | 2 8 6 | 3  9 1 |
| 3 8  9   | 4 1 7 | 2  6 5 |
| 1 6  2   | 3 9 5 | 8  7 4 |
+----------+-------+--------+

Play this puzzle online at the Daily Sudoku site
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arkietech



Joined: 31 Jul 2008
Posts: 1686
Location: Northwest Arkansas USA

PostPosted: Thu Jan 10, 2013 4:53 pm    Post subject: Reply with quote

Marty R. wrote:
Converting jack02's position to grid style.

Code:

+----------+-------+--------+
| 9 14 14  | 6 5 8 | 7  2 3 |
| 5 2  8   | 7 3 9 | 4  1 6 |
| 6 3  7   | 1 2 4 | 9  5 8 |
+----------+-------+--------+
| 2 7  3   | 8 6 1 | 5  4 9 |
| 4 15 156 | 9 7 3 | 16 8 2 |
| 8 9  16  | 5 4 2 | 16 3 7 |
+----------+-------+--------+
| 7 45 45  | 2 8 6 | 3  9 1 |
| 3 8  9   | 4 1 7 | 2  6 5 |
| 1 6  2   | 3 9 5 | 8  7 4 |
+----------+-------+--------+

Play this puzzle online at the Daily Sudoku site


This is an invalid puzzle. The original Jan 7 puzzle has a 1 in r6c3 as a clue this puzzle has multiple solutions
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Thu Jan 10, 2013 5:04 pm    Post subject: Reply with quote

In the original puzzle R6C3 is given as 1 and it has a unique solution.

Keith
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jack02



Joined: 08 Jan 2013
Posts: 5

PostPosted: Fri Jan 11, 2013 2:08 am    Post subject: Reply with quote

I'm not sure if I should feel seriously stupid or slightly clueless (i.e. missing a Clue!)...
Thanks for the Help!
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Marty R.



Joined: 12 Feb 2006
Posts: 5063
Location: Rochester, NY, USA

PostPosted: Fri Jan 11, 2013 2:48 am    Post subject: Reply with quote

jack02 wrote:
I'm not sure if I should feel seriously stupid or slightly clueless (i.e. missing a Clue!)...
Thanks for the Help!


Forget it. We've all done similar things. In my case, way too frequently. Embarassed
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