Magic Squares
Jason Menard
Sheriff
Posts: 6450
posted 13 years ago
Is anyone familiar with Magic Squares? To quote from the previous link:
So given that definition, a 3x3 magic square would be:
8 1 6
3 5 7
4 9 2
Notice that the sum of each row, column, and the two main diagonals is equal to 3(3^2+1)/2 = 15.
The challenge is to write a small program that can produce a magic square for a given input n.
[ June 01, 2003: Message edited by: Jason Menard ]
A magic square is an arrangement of the numbers from 1 to n^2 (nsquared) 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.
So given that definition, a 3x3 magic square would be:
8 1 6
3 5 7
4 9 2
Notice that the sum of each row, column, and the two main diagonals is equal to 3(3^2+1)/2 = 15.
The challenge is to write a small program that can produce a magic square for a given input n.
[ June 01, 2003: Message edited by: Jason Menard ]
Michael Morris
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Eric Pascarello
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Jason Menard
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James Chegwidden
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posted 13 years ago
Yes, I give out a magic square problem every year, usually in my C and C++ classes. Years ago I found a book on number puzzles written in Pascal. One of those puzzles was on magic squares and how to create them as well as finding the magic number.
There is a technique to create odd number magic squares. This is a relatively straight forward. There is a way to create even magic square with algorithm but you cannot create a magic square for any even number just odd ones.
There is a technique to create odd number magic squares. This is a relatively straight forward. There is a way to create even magic square with algorithm but you cannot create a magic square for any even number just odd ones.
Author and Instructor, my book
Francis Siu
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Posts: 867
posted 13 years ago
Is anyone familiar with Magic Squares?
yes,here
But just play it on paper with my brother who teach me how to play.
I can not remember the square is 7*7,8*8 or 9*9,10*10
But I think it is difficult to use programme to do it.
Are there any presents if anyone can write it out?
[ June 01, 2003: Message edited by: siu chung man ]
yes,here
But just play it on paper with my brother who teach me how to play.
I can not remember the square is 7*7,8*8 or 9*9,10*10
But I think it is difficult to use programme to do it.
Are there any presents if anyone can write it out?
[ June 01, 2003: Message edited by: siu chung man ]
Francis Siu
SCJP, MCDBA
John Lee
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Arjun Shastry
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posted 13 years ago
Originally posted by Capablanca Kepler:
I did this program few months back.i will post as soon as I get it.My approach was:
1)Write the first number in the first row in the middle.
2)Move straight down and one right.
3)Move diagonally right up as possible.
4)If you are in first row go to 2.
5)If its a last column,move one row up,first element and goto step 3.
6)If its not the last column,move one down,and goto step 3.
MH
Jason Menard
Sheriff
Posts: 6450
posted 13 years ago
But that only works for magic squares where n is an odd number. The same algorithm won't work if n is even.
Originally posted by Capablanca Kepler:
I did this program few months back.i will post as soon as I get it.My approach was:
1)Write the first number in the first row in the middle.
2)Move straight down and one right.
3)Move diagonally right up as possible.
4)If you are in first row go to 2.
5)If its a last column,move one row up,first element and goto step 3.
6)If its not the last column,move one down,and goto step 3.
But that only works for magic squares where n is an odd number. The same algorithm won't work if n is even.
James Chegwidden
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posted 13 years ago
Yes, there are two ways to create magic squares. The way that was mentioned works for odd even magic squares use a sightly different formula.
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James Chegwidden
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posted 13 years ago
Ok, I dug up some old papers.
Odd cell MS 3, 5, 7, 9 diagonal arrow method De la Loubere procedure
Even cell MS 4, 8, 12, 16 crossdiagonal method
Odd cell MS 3, 5, 7, 9 diagonal arrow method De la Loubere procedure
Even cell MS 4, 8, 12, 16 crossdiagonal method
Author and Instructor, my book
Richard Hernandez
Greenhorn
Posts: 7
posted 13 years ago
Anyone know how to write a simple 3*3 or 5*5 magic square with the number starting as odd?
I am new to java this year,and this one[code] is bugging me.
I am new to java this year,and this one[code] is bugging me.
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