The Perfect Solution For the
MAGIC - SQUARE

. ...KOREAN(ѱ)... . Since July 1997

-- Yes, you can make all Magic Squares !! --

Stories

History of Magic Square
Suzanne Alejandre's Lo Shu Magic Square homepage shows a detail legend of Lo Shu in China. Magic squares have been around for over 3,000 years..

What's a Magic Square?
The following definition is a quote from Allan Adler's What is a Magic Square? homepage.

A magic square is an arrangement of the numbers from 1 to n^2 (n-squared) in an nxn matrix, with each number occurring exactly once, and such that the sum of the entries of any row, any column, or any main diagonal is the same. It is not hard to show that this sum must be n(n^2+1)/2.

What I'm saying is.. .
When I was young I saw a 3x3 magic square. It was just a kind of puzzle for me. As time passed, I saw the solution for magic squares of odd-series and some multiples of four, and I changed my mind. I started to find out the solution for all numbers. I tried to look for any books written on magic squares, but I could not find a regular solution for n=6,10,14,.. at anywhere. Even somebody said 'It's an unsolved mystery'. But, I found out the principle of constructing squares for other sizes and checked that sums are correct by using a computer. Perhaps a man I don't know has already solved this mystery. I hope that more information and news are exchanged at this site. Anyway, I am content to have solved it by myself. Now, the magic square is no more an unsolved mystery. What I'm saying here is "It's Not Impossible!!".


Solutions for the 3 types of Magic Square

If you remember solutions down here, You can construct any magic square(n>2).

The odd number series(n=3,5,7,9,...)
This solution that I'm going to demonstrate is just one of the common things that many people know.

A multiple of 4 series(n=4,8,12,...)
This solution is known, also. I have another method that is more simple and general, because this idea applies to the solution of the other sizes(n=6,10,...) more easily than other methods

The other sizes series(n=6,10,14,...)
Only a few Magic Squares of this series have been known till now. Even if this mystery already has been solved, my solution will be a good general solution to know.

One more solution of The other sizes series
Cheerio, GijsjebertiX introduces the solution.

Even though I don't explain the principle in detail, You can understand the idea well enough. If you have comments and suggestions, please mail to Kwon Young Shin.


Samples

The source program in C-language
This is a source program that I compiled and checked the Magic Squares using turbo-c 2.0 on PC. If you change some source code, You can create more magic squares even on other computers.

Magic Square samples(n=11,12,14,16,18,22,26,30)


Other Magic Square links

Mutsumi Suzuki's Magic Square Page

Suzanne Alejandre's Magic Square Page

Thanks to Julianna Oh for helping me.

Shin, Kwon Young - brainstm@chollian.net
Last Update : 24 Jan 1998

Go to Shin's Flash Puzzle Game homepage.