How can you be sure that blasted Sudoku is solvable? And is there more than one way to skin a particular puzzle? Mathematicians Agnes M. Herzberg and M. Ram Murty explore these questions in their article, “Sudoku Squares and Chromatic Polynomials,” published in the June/July 2007 issue of the Notices of the American Mathematical Society.
Using a branch of mathematics called graph theory, Herzberg and Murty analyze these highly addictive newspaper and web puzzles, which are a 9 x 9 grid where some of the entries have a number filled in from 1 to 9. To complete the puzzle, one fills in the grid such that every row, every column, and every one of the smaller 3 x 3 sub-grids contain the digits from 1 to 9 exactly once.
Those who would like to brush up on their Latin squares (what’d you call me?), colorful chromatic polynomials, and Möbius functions can see the article here.
So the burning question is, what’s the minimum number of given entries needed to ensure that a puzzle has a unique solution? The authors conclude that no one knows. But as many Sudoku enthusiasts know, 17 is a safe bet. And the more difficult puzzles have fewer numbers given.
More about the Sudoko paper in this press release at EurekaAlert!
Web Sudoku has free online puzzles waiting for you to solve. And don’t worry about running out, there’s 5,472,730,538 different ones to choose from.
Jorge,
Yes, these sudoku puzzles are highly addictive. I guess there are worse addictions in life, but I oftentimes have tell myself: enough is enough.
How about you, Jorge?
Bruce
I tried solving one of these not long ago … and failed miserably! I consider myself a logical person. But this puzzle had me very flustered.
Still, it’s fascinating. Have you tried to work the one you’re using as an illustration on this post?
Fess up, Jorge! Do you know how to work these things? What’s the secret?
I recommend checking out the easier ones to start with that have more numbers filled in. Anyone have a good Sudoku website? I thought Web Sudoku was pretty good, with lots of easier ones.
Wikipedia has some strategies on solving Soduko puzzles.
For those looking for something even more challenging, the Seattle Times recently ran a story called “What’s the next Sudoku? Now there’s a puzzle.“
I looked at Wiki’s puzzle-solving strategies. You mean it’s kosher to write the possibilities into the squares? Uh oh. I see many hours of puzzling ahead for me.
Deborah
This just in … Sci-Doku … a sudoku puzzle that uses letters instead of numbers.
Deborah (et al.),
There are a few basic tricks and some more exotic ones that can cut down on your time quite a bit. There are even inexpensive books available at B&N and others that show you how to do it. “Guessing,” i.e. putting in a random digit and see if it works out, is considered bad form. But you can put in the candidates that are left after eliminating possibilities, and cross them out as you eliminate more and more. Otherwise, there’s no hope.
I work the “hard” category of puzzles on websudoku.com and always time myself. Even after hundreds of puzzles, I’ve never gotten even close to the median time!! I don’t think I could fill in the squares with random digits in the shortest times given. websudoku lets you fill in multiple numbers on-screen and then take them out as you eliminate more and more possibilities (use the Options button for this). Click on the FAQS link on websudoku to get some tips that really help get you started. It also keeps your score on your computer, so you know your average time for each category.
My wife works the “evil” category, about one a day. She, too, is way behind the power curve. I’ve tried the evil a few times, but it’s too much like drudgery. To me, “hard” is challenging but still fun.
Ray
For everybody who wants to try out something new in sudoku, try shendoku, using the sudoku rules but playing two people, one against the other, like battleshipps. They have a free version to download at http://www.shendoku.com/sample.pdf . Anything else they are bringing out or they are working on you can find at http://www.shendoku.com or at they´r blog http://www.shendoku.blogspot.com . Have fun, I am.
Yeah,
This looks like extrim sudoku. Better start with easy variants. I can suggest this site http://the-sudoku.net to find more Sudokus