In college I took a class on artificial intelligence, and the final project was to write a program that could solve sudoku puzzles. Ever since then I've been a fan of sudoku and do a few puzzles every now and then. Last week I found out one of my coworkers has a website with printable puzzles and one of the sections are sudoku puzzles. How cool is that?
If you like puzzles, check out his site, he even lives down the street from me :)
I love Sudoku puzzles and work several most every day. Well, not the hard ones. I am finishing out the medium ones in a book that I have done all the hard and extra hard ones and my wife has done all the easy ones. I have often wanted to write a program or somehow figure out how many distinct solutions there are. The possible puzzles that start at a different point of numbers showing even with the same solution would probably be impossible to figure out. But finding the number of solutions is probably possible. I have noticed that the rows and columns can be interchanged to create a new solution. For example, if A, B, C, etc., are blocks of nine numbers (1 through 9) that work as a solution, if ... A B C D E F G H I works, then D E F G H I A B C also works, as does B C A E F D H I G Try it on the next puzzle you solve. That would have to be taken into consideration if one tried to find all possible solutions. They are similar solutions, but unique, I suppose. Maybe a cluster of solutions. I have always thought that writing a program to solve Sudoku puzzles would be fairly easy. Am I right? When I work a Sudoku puzzle, I start by filling in all the obvious numbers and then lightly pencil in the possibilities in each remaining block and go from there. I would think that would be how you would have a program do it also. Such is the beauty of math, that you can enjoy something on a simple, surface level, but there is so much going on underneath. Math is just another thing that convinces me that there is a supreme being that created all this. Otherwise, there would be little order to anything.
" I have always thought that writing a program to solve Sudoku puzzles would be fairly easy. Am I right?"
It is once someone teaches you the technique, see here for details.
Alienated: The interchanges you describe are sometimes called transpositions. Mathematicians who have studied sudoku have measured the number of unique puzzle configurations, taking transpositions into account. According to the Wikipedia article on Mathematics of Sudoku, one measure of "essentially different" or symmetrically distinct solutions puts it at 5,472,730,538.
Writing programs to construct or solve valid Sudoku isn't terribly difficult. What I found difficult (in constructing the puzzles for my site, krazydad, is giving the puzzles accurate difficulty rankings. This required writing a separate, more elaborate solver that mimics the way humans solve puzzles. There are some other puzzle varieties I found more challenging to write constructors for (I'm still working on "Nurikabe" puzzles, which have challenged me for years).
Well, that's cool that the website designers lives down the street from you. Other than that I'm just here to say that while I love puzzles of all kinds, I have never had the mental energy to even atempt to solve a sudoku one. I guess it's because math is my weak subject, but I wish I was smart enough to do them.
The concept of artificial intelligence solving them is interesting to me, though.