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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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 Posted: Thu Mar 09, 2006 4:18 am Post subject: A very tough minimal sudoku |
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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 |
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someone_somewhere
Joined: 07 Aug 2005
Posts: 275
Location: Munich
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| Posted: Sun Mar 12, 2006 2:12 pm Post subject: |
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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, |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Mar 12, 2006 10:09 pm Post subject: Position 1 |
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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 |
+----------------------+----------------------+----------------------+
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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 |
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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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| Posted: Sun Mar 12, 2006 11:12 pm Post subject: There's a "coloring" move on the "7"s |
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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 |
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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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| Posted: Mon Mar 13, 2006 12:30 am Post subject: R1C9 = 9 |
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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 |
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someone_somewhere
Joined: 07 Aug 2005
Posts: 275
Location: Munich
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| Posted: Mon Mar 13, 2006 8:59 am Post subject: |
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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, |
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