All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
A 2007 Problem (Posted on 2007-01-04) Difficulty: 3 of 5
A magic square of order n is a square array of nē consecutive integer numbers (usually, but not neccessarily, from 1 to nē) arranged so the sum of the numbers in any horizontal, vertical, or main diagonal line is always the same number, called the magic constant.

For which values of n are there magic squares of order n, with a magic constant of 2007?

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Only positive numbers. Don't ask me to actually find them. | Comment 1 of 2

The numbers 1 to n^2 sum to n^2(n^2 +1)/2 so each row sums to n(n^2 +1)/2.  This is not equal to 2007 for any n but is negative for positive integers 15 or less so it may be possible to add a constant, a, to each number.

Each row must then sum to n^2(n^2 +1)/2 + na.
Setting this equal to 2007 yields integers solutions for a for only n={1,2,3,6,9}

I know there is no order 2 magic square and order 1 doesn't make much sense.  So there are 3 solutions for n: {3,6,9}.

The corresponding values of a are {664, 316, 182}.


  Posted by Jer on 2007-01-05 13:33:38
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information