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 

can there be 2 solutions ?

 
Post new topic   Reply to topic    dailysudoku.com Forum Index -> General discussion
View previous topic :: View next topic  
Author Message
smriti
Guest





PostPosted: Tue Apr 25, 2006 1:55 pm    Post subject: can there be 2 solutions ? Reply with quote

Hello,

Can there be 2 or more solutions for a sudoku ?
and on what basis is the difficulty level measured ?
thank you in advance
Back to top
David Bryant



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

PostPosted: Tue Apr 25, 2006 9:10 pm    Post subject: Multiple solutions; difficulty ratings Reply with quote

Hi, smriti!

A well-formed 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" (x-wing, xy-wing, 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
Back to top
View user's profile Send private message Send e-mail Visit poster's website
Robert Ferre



Joined: 09 Apr 2006
Posts: 10

PostPosted: Wed Apr 26, 2006 12:08 am    Post subject: Unique helps Reply with quote

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.
Back to top
View user's profile Send private message
Marty R.



Joined: 12 Feb 2006
Posts: 5176
Location: Rochester, NY, USA

PostPosted: Wed Apr 26, 2006 5:12 pm    Post subject: Reply with quote

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 1-9 with no duplicates. However, I know that the puzzle had one and only one solution, so I erased the whole thing and started over.
Back to top
View user's profile Send private message
Display posts from previous:   
Post new topic   Reply to topic    dailysudoku.com Forum Index -> General discussion 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