Can someone explain how to work out the solution

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Can someone explain how to work out the solution

Postby Nicholasstj » Thu Jul 02, 2015 9:58 pm

The puzzle is:
7643528--
259817364
1839--572
9-567--38
-785---4-
-----875-
43-7---85
8-74-56-3
5-6-834-7
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Re: Can someone explain how to work out the solution

Postby JasonLion » Fri Jul 03, 2015 2:08 am

That puzzle does not have a valid solution.
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Re: Can someone explain how to work out the solution

Postby JC Van Hay » Fri Jul 03, 2015 7:12 am

Code: Select all
+----------------+------------------+-------------------+
| 7   6     4    | 3     5      2   | 8     19     19   |
| 2   5     9    | 8     1      7   | 3     6      4    |
| 1   8     3    | 9     46     46  | 5     7      2    |
+----------------+------------------+-------------------+
| 9   124   5    | 6     7      14  | 12    3      8    |
| 36  7     8    | 5     239    19  | 129   4      169  |
| 36  4-12  (12) | (12)  349-2  8   | 7     5      69-1 |
+----------------+------------------+-------------------+
| 4   3     12   | 7     269    169 | 19-2  8      5    |
| 8   129   7    | 4     29     5   | 6     19(2)  3    |
| 5   129   6    | 12    8      3   | 4     19(2)  7    |
+----------------+------------------+-------------------+
Claiming : 2C8 excludes 2r7c7;
Naked Pair : (12)r6c34 excludes 1r6c29, 2r6c25;
Singles to the contradiction [The puzlle has 0 solution].
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Re: Can someone explain how to work out the solution

Postby daj95376 » Fri Jul 03, 2015 4:48 pm

JasonLion wrote:That puzzle does not have a valid solution.

For me, the (#) cells with <12> lead to an early contradiction.

Code: Select all
 *------------------------------------------------------------*
 | 7     6     4     |  3     5     2     | 8     19    19    |
 | 2     5     9     |  8     1     7     | 3     6     4     |
 | 1     8     3     |  9     46    46    | 5     7     2     |
 |-------------------+--------------------+-------------------|
 | 9     124   5     |  6     7     14    | 12    3     8     |
 | 36    7     8     |  5     239   19    | 129   4     169   |
 | 36    4-12 #12    | #12    349-2 8     | 7     5     69-1  |
 |-------------------+--------------------+-------------------|
 | 4     3    #12    |  7     69-2  69-1  | 129   8     5     |
 | 8     129   7     |  4     29    5     | 6     129   3     |
 | 5     9-12  6     | #12    8     3     | 4     129   7     |
 *------------------------------------------------------------*

 Naked  Pair (12) in r6c3,r6c4            =>  -12 r6c259
 Remote Pair (12) in r7c3,r6c3,r6c4,r9c4  =>  -12 r7c5,r7c6,r9c2
 Naked Single                             =>  =4  r6c2
 Naked Single                             =>  =9  r9c2

Leaving the following grid:

Code: Select all
 *--------------------------------------------------*
 | 7    6    4    | 3    5    2    | 8    19   19   |
 | 2    5    9    | 8    1    7    | 3    6    4    |
 | 1    8    3    | 9    46   46   | 5    7    2    |
 |----------------+----------------+----------------|
 | 9   #12   5    | 6    7    14   |#12   3    8    |
 | 36   7    8    | 5    239  19   | 129  4    169  |
 | 36   4   #12   | 12   39   8    | 7    5    69   |
 |----------------+----------------+----------------|
 | 4    3   #12   | 7   @69  @69   | 129  8    5    |
 | 8    12   7    | 4    29   5    | 6    129  3    |
 | 5    9    6    | 12   8    3    | 4    12   7    |
 *--------------------------------------------------*

 Remote Pair (12) in r7c3,r6c3,r4c2,r4c7  =>  -12  r7c7
 Naked  Pair (69) in r7c5,r7c6            =>  -  9 r7c7

 Contradiction:  r7c7 is empty

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Re: Can someone explain how to work out the solution

Postby Leren » Fri Jul 03, 2015 8:51 pm

OK the puzzle has no solution, but I've never seen a puzzle with 53 clues before. Common sense tells me that it's a partial solution where a mistake has been made.

Either Nicholasstj has to post the original puzzle, or the puzzle creators can change one or two clues around so that the puzzle has one solution. Any takers ?

Leren
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Re: Can someone explain how to work out the solution

Postby daj95376 » Fri Jul 03, 2015 9:26 pm

Leren wrote:OK the puzzle has no solution, but I've never seen a puzzle with 53 clues before. Common sense tells me that it's a partial solution where a mistake has been made.

Either Nicholasstj has to post the original puzzle, or the puzzle creators can change one or two clues around so that the puzzle has one solution. Any takers ?

If you "disable" all of the solved cells in [b1], then the puzzle can be solved.

Code: Select all
 +-----------------------+
 | . . . | 3 5 2 | 8 . . |
 | . . . | 8 1 7 | 3 6 4 |
 | . . . | 9 . . | 5 7 2 |
 |-------+-------+-------|
 | 9 . 5 | 6 7 . | . 3 8 |
 | . 7 8 | 5 . . | . 4 . |
 | . . . | . . 8 | 7 5 . |
 |-------+-------+-------|
 | 4 3 . | 7 . . | . 8 5 |
 | 8 . 7 | 4 . 5 | 6 . 3 |
 | 5 . 6 | . 8 3 | 4 . 7 |
 +-----------------------+

   c7b6  Locked Candidate 1              -2    r7c7

   c67   X-Wing                          -9    r5c59,r7c5

 <29+1>  XYZ-Wing r5c7/r4c7+r5c6         -1    r5c9

 <23+1>  XY-Wing  r5c5/r5c1+r6c4         -1    r5c6,r6c23

Solution:

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

Comparing it to the original puzzle results in the solutions of r3c1 and r3c3 being swapped.

Code: Select all
 Original Puzzle Provided
 +-----------------------+
 | 7 6 4 | 3 5 2 | 8 . . |
 | 2 5 9 | 8 1 7 | 3 6 4 |
 | 1 8 3 | 9 . . | 5 7 2 |
 |-------+-------+-------|
 | 9 . 5 | 6 7 . | . 3 8 |
 | . 7 8 | 5 . . | . 4 . |
 | . . . | . . 8 | 7 5 . |
 |-------+-------+-------|
 | 4 3 . | 7 . . | . 8 5 |
 | 8 . 7 | 4 . 5 | 6 . 3 |
 | 5 . 6 | . 8 3 | 4 . 7 |
 +-----------------------+

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Re: Can someone explain how to work out the solution

Postby Leren » Fri Jul 03, 2015 11:44 pm

Hi Danny, nice solution - just what I was looking for. If you add one correct clue in Box 1 the XYZ wing and XY wing can be replaced by a Skyscraper (2) r67c3, r69c4 => - 2 r7c5, r9c2, which is possibly closer to the puzzle difficulty you may find in a Sudoku book or newspaper.

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Re: Can someone explain how to work out the solution

Postby m_b_metcalf » Sat Jul 04, 2015 10:17 am

Leren wrote:OK the puzzle has no solution, but I've never seen a puzzle with 53 clues before. Common sense tells me that it's a partial solution where a mistake has been made.

Either Nicholasstj has to post the original puzzle, or the puzzle creators can change one or two clues around so that the puzzle has one solution. Any takers ?

Leren


Code: Select all
 7 6 4 3 5 2 8 . .
 2 5 9 8 1 7 3 6 4
 3 8 1 9 . . 5 7 2
 9 . 5 6 7 . . 3 8
 . 7 8 5 . . . 4 .
 . . . . . 8 7 5 .
 4 3 . 7 . . . 8 5
 8 . 7 4 . 5 6 . 3
 5 . 6 . 8 3 4 . 7
No. of givens =  53

singles found 1 solution


Regards,

Mike Metcalf
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Re: Can someone explain how to work out the solution

Postby Leren » Sat Jul 04, 2015 11:27 am

m_b_metcalf wrote:
Leren wrote:OK the puzzle has no solution, but I've never seen a puzzle with 53 clues before. Common sense tells me that it's a partial solution where a mistake has been made.

Either Nicholasstj has to post the original puzzle, or the puzzle creators can change one or two clues around so that the puzzle has one solution. Any takers ?

Leren


Code: Select all
 7 6 4 3 5 2 8 . .
 2 5 9 8 1 7 3 6 4
 3 8 1 9 . . 5 7 2
 9 . 5 6 7 . . 3 8
 . 7 8 5 . . . 4 .
 . . . . . 8 7 5 .
 4 3 . 7 . . . 8 5
 8 . 7 4 . 5 6 . 3
 5 . 6 . 8 3 4 . 7
No. of givens =  53

singles found 1 solution


Regards,

Mike Metcalf

Yes, Danny showed that by swapping 13 in r3c13 the puzzle has 1 solution. In fact he showed that you can remove all clues in Box 1. Perhaps the next challenge is to put the puzzle in minimal form which, if I understand the term correctly, is to remove as many clues as possible whilst retaining the single solution. Good luck to the puzzle creators in this regard.

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Re: Can someone explain how to work out the solution

Postby m_b_metcalf » Sat Jul 04, 2015 11:43 am

Leren wrote: In fact he showed that you can remove all clues in Box 1.


Not quite:
Code: Select all
 0 0 0 3 5 2 8 0 0
 0 0 0 8 1 7 3 6 4
 0 0 0 9 0 0 5 7 2
 9 0 5 6 4 0 0 3 8
 0 7 8 5 0 0 0 4 0
 0 0 0 0 0 8 9 5 0
 4 3 0 7 0 0 0 8 5
 8 0 7 4 0 5 6 0 3
 5 0 6 0 8 3 4 0 7
No. of givens =  44

brute found 3 solution(s)
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Re: Can someone explain how to work out the solution

Postby m_b_metcalf » Sat Jul 04, 2015 11:59 am

Leren wrote:Perhaps the next challenge is to put the puzzle in minimal form which, if I understand the term correctly, is to remove as many clues as possible whilst retaining the single solution.


Here is a minimal form with 28 clues:

Code: Select all
 . . . 3 5 . 8 . .
 . . . 8 . 7 3 6 4
 1 . . 9 . . 5 7 .
 9 . 5 6 4 . . 3 8
 . 7 8 . . . . 4 .
 . . . . . . 9 . .
 . 3 . 7 . . . 8 .
 . . 7 4 . . . . .
 5 . . . . . . . .

Thre are others that are likely to be smaller.
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Re: Can someone explain how to work out the solution

Postby m_b_metcalf » Sat Jul 04, 2015 2:57 pm

m_b_metcalf wrote:Thre are others that are likely to be smaller.


Code: Select all
 . . 4 . . 2 8 . .
 . 5 9 8 . 7 . 6 .
 . . . . . . . 7 2
 9 . 5 6 . . . 3 .
 . 7 8 5 . . . . .
 . . . . . . 7 . .
 . 3 . 7 . . . 8 .
 . . . 4 . 5 6 . .
 . . . . . . 4 . .   25 clues
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Re: Can someone explain how to work out the solution

Postby daj95376 » Sat Jul 04, 2015 4:13 pm

m_b_metcalf wrote:
Leren wrote: In fact he showed that you can remove all clues in Box 1.


Not quite:
Code: Select all
 0 0 0 3 5 2 8 0 0
 0 0 0 8 1 7 3 6 4
 0 0 0 9 0 0 5 7 2
 9 0 5 6 4 0 0 3 8
 0 7 8 5 0 0 0 4 0
 0 0 0 0 0 8 9 5 0
 4 3 0 7 0 0 0 8 5
 8 0 7 4 0 5 6 0 3
 5 0 6 0 8 3 4 0 7
No. of givens =  44

brute found 3 solution(s)


Try placing <7> in r4c5 and r6c7.

Code: Select all
 +-----------------------+
 | . . . | 3 5 2 | 8 . . |
 | . . . | 8 1 7 | 3 6 4 |
 | . . . | 9 . . | 5 7 2 |
 |-------+-------+-------|
 | 9 . 5 | 6 7 . | . 3 8 |
 | . 7 8 | 5 . . | . 4 . |
 | . . . | . . 8 | 7 5 . |
 |-------+-------+-------|
 | 4 3 . | 7 . . | . 8 5 |
 | 8 . 7 | 4 . 5 | 6 . 3 |
 | 5 . 6 | . 8 3 | 4 . 7 |
 +-----------------------+

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