dailysudoku.com Forum Index dailysudoku.com
Discussion of Daily Sudoku puzzles
 
 FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

A very tough minimal sudoku

 
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Other puzzles
View previous topic :: View next topic  
Author Message
David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Thu Mar 09, 2006 4:18 am    Post subject: A very tough minimal sudoku Reply with quote

Here's a very difficult 17-clue sudoku puzzle. Someone_somewhere sent me this puzzle in a private message. I'm not yet sure how to reason my way through to the solution.
Code:
6.2.5....
.....4.3.
.........
43...8...
.1....2..
......7..
5..27....
.......81
...6.....

Oh -- s_s called this a "zen" sudoku, apparently implying that it can be solved if one thinks about it (becomes it?) hard enough. dcb
Back to top
View user's profile Send private message Send e-mail Visit poster's website
someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Sun Mar 12, 2006 2:12 pm    Post subject: Reply with quote

Yes, I called it Zen.
No single response in this forum is confirming it's name.
I know how to get to the solution, but it takes a long time, like in the Zen training. No brute force is needed.

If someone makes/made some progress on it, share it with us.

see u,
Back to top
View user's profile Send private message
keith



Joined: 19 Sep 2005
Posts: 3179
Location: near Detroit, Michigan, USA

PostPosted: Sun Mar 12, 2006 10:09 pm    Post subject: Position 1 Reply with quote

This is about the toughest puzzle I have ever tried.

I found six pinned squares, and a pair in column 9. Then after another seven moves (intersections to remove possibilities, not to solve squares), I get to this:

Code:



+----------------------+----------------------+----------------------+
| 6      4789   2      | 13789  5      379    | 1489   179    49     |
| 1789   5789   15789  | 1789   169    4      | 1689   3      2      |
| 13789  4789   134789 | 1789   169    2      | 14689  15679  4569   |
+----------------------+----------------------+----------------------+
| 4      3      5679   | 1579   2      8      | 169    1569   569    |
| 789    1      56789  | 34579  349    35679  | 2      4569   38     |
| 289    25689  5689   | 13459  1349   3569   | 7      14569  38     |
+----------------------+----------------------+----------------------+
| 5      4689   134689 | 2      7      139    | 3469   69     469    |
| 2379   2679   3679   | 3459   349    359    | 3569   8      1      |
| 139    49     1349   | 6      8      1359   | 3459   2      7      |
+----------------------+----------------------+----------------------+



I have played with this for a while, and I have no clue! The best I can suggest is to examine the squares that could be <4>.

Let's call this "Position 1". What next?

Keith
Back to top
View user's profile Send private message
David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Sun Mar 12, 2006 11:12 pm    Post subject: There's a "coloring" move on the "7"s Reply with quote

Hi, Keith!

I think we can eliminate one more possibility from the grid using "standard" methods. After that I think we'll have to start using "double-implication chains."
Code:
+----------------------+----------------------+----------------------+
| 6      4789   2      | 13789  5      379B   | 1489   179A   49     |
| 1789   5789   15789  | 1789   169    4      | 1689   3      2      |
| 13789  4789   134789 | 1789   169    2      | 14689  15679a 4569   |
+----------------------+----------------------+----------------------+
| 4      3      5679c  | 1579C  2      8      | 169    1569   569    |
| 789    1      56789  | 34579  349    35679b | 2      4569   38     |
| 289    25689  5689   | 13459  1349   3569   | 7      14569  38     |
+----------------------+----------------------+----------------------+
| 5      4689   134689 | 2      7      139    | 3469   69     469    |
| 2379   2679   3679   | 3459   349    359    | 3569   8      1      |
| 139    49     1349   | 6      8      1359   | 3459   2      7      |
+----------------------+----------------------+----------------------+

There are three binary chains in the "7"s, marked Aa, Bb, and Cc above.

1. r1c8 = 7 ==> r1c6 <> 7 ==> r5c6 = 7 ==> r4c4 <> 7 ==> r4c3 = 7 ==> r3c3 <> 7.
2. r1c8 <> 7 ==> r3c8 = 7 ==> r3c3 <> 7.

So we can eliminate the possible "7" at r3c3.

I'm still working on my next move. dcb
Back to top
View user's profile Send private message Send e-mail Visit poster's website
David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Mon Mar 13, 2006 12:30 am    Post subject: R1C9 = 9 Reply with quote

I'm starting from the position previously posted, with the "7" removed from r3c3. We can demonstrate that r1c9 <> 4 as follows.

r1c9 = 4 ==> {6, 9} pair in r7c8&9 ==> {3, 4, 5, 9} quad in r8c456&7.

Making these eliminations the matrix looks like this.

Code:
  6    789     2    13789   5    379    189    179    4
1789  5789   15789  1789   169    4    1689     3     2
13789 4789   13489  1789   169    2    1689   15679  569
  4     3    5679   1579    2     8     169   1569   569
 789    1    56789  34579  349  35679    2    4569   38
 289  25689  5689   13459 1349  3569     7    14569  38
  5    48    1348     2     7    13     34     69    69
 27    267    67    3459   349   359    35      8     1
 139   49    1349     6     8   1359    345     2     7


But now we can spot another quad, {4, 7, 8, 9} in column 2. Making this elimination in the column also reveals that the "7" in column 2 must lie in the top left 3x3 box, so we can simplify the matrix like this.

Code:
  6    789     2    13789   5    379    189    179    4
 189    5     189   1789   169    4    1689     3     2
1389  4789   13489  1789   169    2    1689   15679  569
  4     3    5679   1579    2     8     169   1569   569
 789    1    56789  34579  349  35679    2    4569   38
 289   26    5689   13459 1349  3569     7    14569  38
  5    48    1348     2     7    13     34     69    69
 27    26     67    3459   349   359    35      8     1
 139   49    1349     6     8   1359    345     2     7


And now we have a series of forced moves:

1. r2c4 = 7 (unique horizontal)
2. r5c6 = 7 (unique vertical)
3. r6c6 = 6 (unique vertical)
4. r6c2 = 2 (sole candidate)
5. r4c3 = 7 (unique horizontal -- because of the "7" at r2c4)
6. r8c3 = 6 (sole candidate)
7. r8c2 = 2 (sole candidate)

But we can't have two "2"s in column 2, so r1c9 <> 4, and r1c9 = 9. This leaves the matrix looking like this.

Code:
  6    478     2    1378    5    37     148    17     9
1789  5789   15789  1789   169    4    1689     3     2
13789 4789   13489  1789   169    2    14689  15679  456
  4     3    5679   1579    2     8     169   1569   56
 789    1    56789  34579  349  35679    2    4569   38
 289  25689  5689   13459 1349  3569     7    14569  38
  5   4689  134689    2     7    139   3469    69    46
2379  2679   3679   3459   349   359   3569     8     1
 139   49    1349     6     8   1359   3459     2     7


From here we can see right away that r7c9 = 4, because if we put in the "6" it will be just like the case with the {6, 9} pair that we analyzed above. So here's where I'm going to leave it for now:

Code:
  6    478     2    1378    5    37     148    17     9
1789  5789   15789  1789   169    4     168     3     2
13789 4789   13489  1789   169    2    1468   1567   56
  4     3    5679   1579    2     8     169   1569   56
 789    1    56789  34579  349  35679    2    4569   38
 289  25689  5689   13459 1349  3569     7    14569  38
  5    689   13689    2     7    139    369    69     4
2379  2679   3679   3459   349   359   3569     8     1
 139   49    1349     6     8   1359    359     2     7
Back to top
View user's profile Send private message Send e-mail Visit poster's website
someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Mon Mar 13, 2006 8:59 am    Post subject: Reply with quote

Thank you, guys.
I used also double implication chains, but ... I had to travel to a couple of other galaxies, until I got to the solution.
It is ZEN.
Hope that you are finding a way, your way ...

Wake me up, when you have something for someone_somewhere

see u,
Back to top
View user's profile Send private message
Display posts from previous:   
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Other puzzles All times are GMT
Page 1 of 1

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum


Powered by phpBB © 2001, 2005 phpBB Group