## Can someone explain how to work out the solution

Post the puzzle or solving technique that's causing you trouble and someone will help

### Can someone explain how to work out the solution

The puzzle is:
7643528--
259817364
1839--572
9-567--38
-785---4-
-----875-
43-7---85
8-74-56-3
5-6-834-7
Nicholasstj

Posts: 1
Joined: 02 July 2015

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

That puzzle does not have a valid solution.

JasonLion
2017 Supporter

Posts: 640
Joined: 25 October 2007
Location: Silver Spring, MD, USA

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

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].
JC Van Hay

Posts: 719
Joined: 22 May 2010

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

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`

_
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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

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
Leren

Posts: 3368
Joined: 03 June 2012

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

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,r6c23Solution: +-----------------------+ | 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 | +-----------------------+`

_
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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

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.

Leren
Leren

Posts: 3368
Joined: 03 June 2012

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

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 . 7No. of givens =  53singles found 1 solution`

Regards,

Mike Metcalf

m_b_metcalf
2017 Supporter

Posts: 9661
Joined: 15 May 2006
Location: Berlin

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

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 . 7No. of givens =  53singles 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.

Leren
Leren

Posts: 3368
Joined: 03 June 2012

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

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 7No. of givens =  44brute found 3 solution(s) `

m_b_metcalf
2017 Supporter

Posts: 9661
Joined: 15 May 2006
Location: Berlin

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

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.

m_b_metcalf
2017 Supporter

Posts: 9661
Joined: 15 May 2006
Location: Berlin

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

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`

m_b_metcalf
2017 Supporter

Posts: 9661
Joined: 15 May 2006
Location: Berlin

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

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 7No. of givens =  44brute 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 | +-----------------------+`

_
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006