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smriti Guest

Posted: Tue Apr 25, 2006 1:55 pm Post subject: can there be 2 solutions ? 


Hello,
Can there be 2 or more solutions for a sudoku ?
and on what basis is the difficulty level measured ?
thank you in advance 

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

Posted: Tue Apr 25, 2006 9:10 pm Post subject: Multiple solutions; difficulty ratings 


Hi, smriti!
A wellformed sudoku puzzle has a unique solution. While it is certainly possible to construct a grid for which two or more "solutions" are possible, such puzzles are generally considered to be invalid.
There are a large number of "difficulty rating" schemes in use, and as far as I'm aware, there is no widely accepted standard for rating the difficulty of a particular puzzle. These schemes are heuristic and usually count the number of "tough" logic steps needed to solve the puzzle. They may also account for the particular kind of logic necessary  a puzzle that does not require "advanced techniques" (xwing, xywing, swordfish, coloring, etc) will generally be considered to be much easier than a puzzle that requires the use of one or more of these more intricate logical processes. dcb 

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Robert Ferre
Joined: 09 Apr 2006 Posts: 10

Posted: Wed Apr 26, 2006 12:08 am Post subject: Unique helps 


If the puzzle indeed has a unique solution, you can use that knowledge to help solve the puzzle. About once a week I run into this situation. There is a rectangle formed by four values, across several of the small squares. Let's say that three of the values (corners of the rectangle) are exactly the same, 2,7. The fourth one is 2,7,5. If all four are 2,7 there would be two solutions, because 2 and 7 could be interchanged for each other. The only way for that to not happen is for that fourth value to be 5. In every case that I have encountered, this has indeed been the case. It works only when three of the corners have the same two numbers, and the fourth corner has three, two of which are the same as the other corners. OF course, if it is a poorly designed puzzle, perhaps there would be two solutions. I suspect, however, that the computer generated puzzles are unique. Counting on that is helpful.
R. 

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Marty R.
Joined: 12 Feb 2006 Posts: 5732 Location: Rochester, NY, USA

Posted: Wed Apr 26, 2006 5:12 pm Post subject: 


Yesterday I was doing one of the "Nightmare" puzzles, and when I was down to only four unsolved cells, they formed a rectangle with the "deadly pattern", with each corner holding a "34." I could have used one value or the other, and "solved" the puzzle, in that the result would have met the requirement of every row, column and box containing 19 with no duplicates. However, I know that the puzzle had one and only one solution, so I erased the whole thing and started over. 

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