Sudoku: Math or Logic?
Sudoku is a number puzzle solved with logic and reasoning, usually seen on newspapers and magazines today. The word Sudoku is short for “Su-ji wa dokushin ni kagiru" meaning "the digits must be single”. A standard puzzle is a 9x9 grid divided into nine 3x3 blocks. Some numbers are given and the purpose of the game is to fill in the rest using only numbers 1 through 9. No number can be repeated in any block, row or column. The difficulty of the puzzle is determined by how many numbers are given and where they are placed. Sudoku was invented by Howard Garns in 1979 and published by Dell Magazine as “Number Place”. It became very popular around 1986 due to a Japanese puzzle company, Nwikoli. In 1997, Wayne Gould discovered Sudoku during a trip to Japan and then tried to bring it to the United States. Gould spent years and years writing a computer program to create puzzles. The New York Post picked it up in April 2005, which is when the puzzle became an international hit accessible to all ages and abilities. “Sudoku, or Su Doku, is the name for a maddeningly addictive Japanese number logic puzzle which has become a bona fide craze in the United States during the past few months”(Monica, 1). According to this article written during the time that Sudoku went viral, Gould was worried that the game would only be popular for a short time, and everyone would forget about it soon. "The glut does concern me. But it's a free market," Gould said. Gould was obviously wrong about this, since the game is still added to newspapers and played all over the world today.
No knowledge of math is necessary to play sudoku. However, by saying that no math is required to solve Sudoku, what is really meant is that no arithmetic is required. “The sort of reasoning that goes into solving a Sudoku puzzle, on the other hand, is at the heart of what mathematics is all about. That so many people will claim to hate doing mathematics while simultaneously enjoying the challenge of solving a puzzle is a source of frustration to those of us in the business”(Rosenhouse, x). In Rosenhouse’s book about Sudoku, the fact that Sudoku is a logic-based game is very much stressed. Since Sudoku has only one correct solution, it is unrealistic to use trial and error or guessing. Many algorithms have been developed and tested to see the efficiency and how fast it is in finding the solution. Logic-based algorithms can efficiently solve easy puzzles but are unable to come up with a solution for harder puzzles.
Strategies
The most fundamental strategy to solve a puzzle is to write down all possible entries that will not contradict the “One Rule”. If a cell ends up having only one possible entry, it should be automatically filled in. Another strategy is to pick a number and a row, column, or block. Then, look at all the cells in the row, column, or block in which the number can be placed without violating the “One Rule”. If the number can only be placed in one cell that cell should be filled in. Once this has been done, the number that was chosen could be eliminated from being a possibility for any other cell.
Another strategy is listing all the candidates from 1 to 9 in each unfilled square and then, for every square whose value v is determined, cross off every v as a possible candidate in the row, column and block to which that square belongs. The values left in each square represent possible values that could be there. A technique that is used a lot towards the end of the puzzle is if eight of the nine numbers in any row, column or block are already determined. The final number has to be the one that is missing.
According to many sources, Sudoku has been a popular game ever since it was first seen in the New York Post and there are various debates on whether or not it will continue to thrive. “Scientists have identified Sudoku as a classic meme - a mental virus which spreads from person to person and sweeps across national boundaries”(Smith, 1). It is indeed a very simple yet addictive game and not just a matter of randomly adding numbers to squares.
Sources
Taking Sudoku Seriously: The Math Behind the World's Most Popular Pencil Puzzle (Book) by Jason Rosenhouse and Laura Taalman
http://www.math.cornell.edu/~mec/Summer2009/Mahmood/Solve.html
http://money.cnn.com/2005/09/19/news/newsmakers/sudoku/
http://www.geometer.org/mathcircles/sudoku.pdf
I never thought that Sudoku was made by Howard Garns, an American. I thought is was created by a Japanese person, but I guess Japan only popularized it. In my opinion I have to disagree with the addictiveness of the game. I find it too frustrating to bring enjoyment after i complete it. I wonder how long Sudoku will last, though. How many possible puzzles can there be before they start repeating? Also in the 1980's did they generate the puzzles with computers and just with people? I think it would be hard to create a unique Sudoku puzzle. In all, Sudoku is definitely not a game I would not play for fun in my spare time.
ReplyDeleteI really enjoyed reading about the background of Sudoku. I found it interesting how no background math knowledge is required to solve Sudoku yet it's all about math still. I never imagined that it was possible to think hard about numbers but without actually doing any solving and just by looking at where the number lies. I also find it cool how popular Sudoku is around the world, especially since it gets fairly frustrating to solve at times.
ReplyDeleteSudoku is a really interesting puzzle that many people can easily get entertained. I found Sudoku's structure fascinating; how a certain number belongs in a precise row or column and how it can act as a domino effect. Also, I have not heard of the second strategy that was mentioned as a way to solve the puzzle. Next time I run into a Sudoku puzzle, I will definitely try that.
ReplyDeleteI like Sudoku,and yes I agree that it is addictive, you play one game and you get hooked. Although it is true that one does not need to be a Math genius to solve the puzzles, I still think there is a strong positive correlation between being good at Maths and Solving the Sudoku, especially the very challenging ones.
ReplyDeleteI never knew the origins of Sudoku and it was very interesting reading about that. I also agree with the other comments on Sudoku's addictiveness. When we solved the puzzles in class. I agree with the statement that Sudoku is mostly a logical puzzle but if I can see how a mathematical genius would be better at this than a person with average mathematical skills. Coming from a family who loves Sudoku, I can understand its popularity and the frustration it can cause people. I loved your explanation of the game, and the pictures that helped illustrate the strategy of listing the numbers.
ReplyDeleteSudoku has always been a somewhat fun thing for me to do. I remember when I was like 10 I did a lot of puzzles. I never knew where it came from so that was very intriguing to me. I still like Sudoku but have not played it in a while. I like how you explained the game and the different strategies!
ReplyDeleteHaving played Sudoku I had never really looked up any information on it. So after reading the bit about its meaning and origin definitely intrigued me. Although I do like the strategies, it just seemed as if they may slow down the game. I personally play to beat a certain time. Obviously that makes it harder but I do like the strategies you mention within your blog post.
ReplyDeletei enjoyed this passage about sudoku and i agree with it being a very addictive game. on the other hand i disagree with the common misconception that it MUST involve numbers. I was introduced to sudoku when i was in elementary school. Children are far more creative and imaginative than adults so it made sense to take out the numbers and replace them with picture, 9 pictures to be exact. this made the puzzles easier to work with as a child. The numbers that are used in typical puzzles aren't necessary. The numbers are symbols that represent a concept of a thing that can't be repeated in a row, column or box. i found it easier to deal with sudoku puzzles when i saw the numbers as symbols rather than things with a numeric value.
ReplyDeleteWhen it comes down to a certain game, I never actually think about how it came about to the world so it was great explaining the origins of it. I often find myself getting stuck certain times which leads to frustration to me but I use some of the strategies that were explained in the post. It's still a big sensation to play as it has expanded to many apps on phones, tablets, as well as to computers and in newspapers so it's something that won't ever be forgotten.
ReplyDeleteBefore this class I honestly haven't even thought of doing a sudoku. I will admit that it was very addicting. After the first class we did one, I went back to my dorm to finish the others. As for the Math or Logic question, I would definelty say its more of a logic thing than a math thing. When you think of math you think of solving equations, finding areas, and other stuff like that. There is obviously a little math to it, but after taking a logic class, I would say it's more of a logic based thing. Because of this class and this read I might consider buying a sudoku book when I'm in the airport.
ReplyDeleteIt was nice to read where sudoku came from. I like to play this game because it is very interesting to me. I also believe this game takes a lot of patience to play. I also kind of find it cool that this game is still popular till this day. It wasn't like one of those games that was popular for a short amount of time and dies off at the end like Gould said.
ReplyDeleteI've always liked to do sudoku puzzles. It was interesting to learn where they originated from. You did a very good job explaining this. Good job
ReplyDeleteSudoku puzzles are one of my favorite things ever. I never thought that it was an american puzzle. Sudoku puzzles are completely addicting for me. I also really enjoyed the background information you gave. The puzzle itself is cool but it's also cool to see the history behind it.
ReplyDeleteI agree that Sudoku is addictive. I liked how you explained the origin of Sudoku. I also liked how you explained the different strategies to finding the one solution to the Sudoku.
ReplyDeleteThe Sudoku is a great topic mathematically and logically. I really like Sudoku puzzles, and the strategy you gave was interesting. The post was well put together and the pictures were great at aiding those who do not know much about Sudoku in understanding the puzzle.
ReplyDelete