Trial and Error Solutions

Advanced methods and approaches for solving Sudoku puzzles

Trial and Error Solutions

Postby ccffpp » Sun Jun 25, 2006 7:26 pm

It is my experience that almost all published sudoku puzzles can be solved by applying to each element the various logic techniques derived from the basic rules--that all nine numbers be present in each 9-element column and row, and non-overlapping 3x3 square. However, occasionally, after partially solving a puzzle, I can complete the solution only by trial and error. Is it true that some puzzles can be completed after a certain point only by trial and error, or, am I ignorant of some advanced logic????

If someone wants to see an example of what I mean, complete the puzzle below---the x's are unfilled elements. You should be able to easily solve this to the point where only the four corner 3x3 blocks remain completely unfilled. Then I think you become stuck without guessing and trying an entry in some remaining unfilled element.

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

Postby keith » Sun Jun 25, 2006 8:24 pm

The puzzle has a pattern called a "BUG". R8C3 must be <8>, and that solves it.

Code: Select all
+-------------+-------------+-------------+
| 6   7   89  | 1   5   4   | 3   29  28  |
| 15  2   15  | 3   9   8   | 4   6   7   |
| 3   89a 4   | 2   7   6   | 89b 5   1   |
+-------------+-------------+-------------+
| 9   3   7   | 8   2   5   | 1   4   6   |
| 4   1   6   | 7   3   9   | 2   8   5   |
| 8   5   2   | 4   6   1   | 7   3   9   |
+-------------+-------------+-------------+
| 7   6   3   | 9   8   2   | 5   1   4   |
| 12  89b 189 | 5   4   3   | 6   7   28  |
| 25  4   58  | 6   1   7   | 89a 29  3   |
+-------------+-------------+-------------+

Or, there is a remote pair on <89>. So, R8C9 and R9C3 cannot be <8>.

Keith
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Postby sirdave » Tue Jun 27, 2006 11:22 pm

Having watched, over the last several months, the rapid development of advanced Sudoku 'logical' methods that solve puzzles that were formerly thought to only be solvable by T&E, it is my guess that the mere act of posting a Sudoku with the suggestion that only T&E can solve it is enough to make some posters here almost giddy with excitement!:D
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Postby tso » Wed Jun 28, 2006 6:29 am

You are right, Sir. But come on -- is this the way of most internet forums? That someone will sign-up, not bother to search through or even browse through the previous 1000's of posts to see that her/his question has been asked and answered 100 times, to admit freely that their experience with the subject is limited but nonetheless, they are here to explain to the rest of us that apparantly, wheels are round? Do newbies post to chess forums and explain the simple way that they've found to always force a checkmate? Do novices post to crossword puzzle forums and ask if guessing is required? Do these people, unaware of exactly how their remote control works, just assume that it's "magic"? Do mathemeticians who have devoted their lives increasing the knowlege and skill, when coming across a problem they cannot solve, proclaim that it can only be solved by guessing?
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Postby sirdave » Mon Jul 03, 2006 7:05 pm

tso wrote:You are right, Sir. But come on -- is this the way of most internet forums? That someone will sign-up, not bother to search through or even browse through the previous 1000's of posts to see that her/his question has been asked and answered 100 times, to admit freely that their experience with the subject is limited but nonetheless, they are here to explain to the rest of us that apparantly, wheels are round? Do newbies post to chess forums and explain the simple way that they've found to always force a checkmate? Do novices post to crossword puzzle forums and ask if guessing is required? Do these people, unaware of exactly how their remote control works, just assume that it's "magic"? Do mathemeticians who have devoted their lives increasing the knowlege and skill, when coming across a problem they cannot solve, proclaim that it can only be solved by guessing?


I hear ya'. Actually, you misunderstood the nature of my post. It was my light-hearted way of expressing exactly what you express above. In other words, it was my way of wondering why on earth, at this point in time, when the concept of T&E is is almost anathema to any discussion in forums like this and almost by the month new solving methods are being discussed, would anyone post in that way (in the Advanced Solving Techniques section no less!)?
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