## Sudoku's maths

Everything about Sudoku that doesn't fit in one of the other sections

### Sudoku's maths

Hi everyone,

Firstly, I'm sorry for my bad english (I'm not from UK or USA). (You can correct me if I do some mistakes btw).

Well, I have to do a report on Sudoku's mathematics as part of my course (i'm running for informatic&maths research schools). I'm not interested in "how to solve a Sudoku" which is a classic question already solved. I'm working on two majors issues as far as sudoku is concerned :
1) How many Sudoku does exist ?
To solve this question, i'm working with the likeness which exists between two Sudoku : for exemple, if you give me a correct Sudoku, and I change every 1 in 2, every 2 in 7, and every 7 in 1, I'll get another correct Sudoku. If I shake (don't know if it is the right word) two 3x9 blocs i'll still have a correct Sudoku.
Thus if I count how many usual transformations exist, I will be able to use the Burnside equation to know how many Sudoku does exist.
This experimentation has already been done by some researchers, and the global answer is about 6.670*10^21 Sudoku ! However, when I do the arithmetic by myself, I get a 6.671*10^21 , which is a significant difference.

2) What is the minimal number of solved squares to have a correct Sudoku ? (I mean, if I give you 81 - 1 = 80 squares, you'll be able to solve this sudoku, if i give you only one square, it will be impossible, and it currently seems that the minimal number is 17 squares, but this is only an empiric result based on the idea that if a 16-solved-square correct Sudoku would exist, there will be a huge number of 17-solved-square correct Sudoku, and it seems there are not so many 17-solved-square correct Sudoku.
I already have this reference : http://www.math.ie/checker.html which is a good one imo. But would you have other articles about this issue for me ?

Thank you for your help, and I hope my post is understandable ^^
Hoetre

Posts: 2
Joined: 26 April 2013

### Re: Sudoku's maths

1) http://www.afjarvis.staff.shef.ac.uk/sudoku/index.html
eleven

Posts: 1847
Joined: 10 February 2008

### Re: Sudoku's maths

Hoetre wrote:This experimentation has already been done by some researchers, and the global answer is about 6.670*10^21 Sudoku ! However, when I do the arithmetic by myself, I get a 6.671*10^21 , which is a significant difference.

The actual number is 6,670,903,752,021,072,936,960, so perhaps your calculation is correct.
blue

Posts: 683
Joined: 11 March 2013

### Re: Sudoku's maths

Yep I know what the actual number is, but I have a different one. I may have forgotten something.

eleven wrote:1) http://www.afjarvis.staff.shef.ac.uk/sudoku/index.html