The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Magic Squares puzzle

Date: Wed, 9 Nov 1994 08:10:14 -0800
From: Rick Jermain
Subject: Math Puzzle Answer needed

Dear Dr. Math,

Can you please send me the Puzzle (and the solution) called the 
Magic Square?

This is a puzzle where you have to arrange numbers so that they add 
up to the same number, vertically, horizontally, and diagonally.

Please help.  Thanks in advance.


Date: Fri, 11 Nov 1994 10:46:24 -0500 (EST)
From: Dr. Ken
Subject: Re: Magic Squares

Hello Rick!

In answer to your question, there are MANY such Magic Squares of all 
kinds of different sizes.  Here's one:

                        8       1       6

                        3       5       7

                        4       9       2

There's an easy way to make them, too, that I believe works for any 
size square.  Start by putting a 1 in the middle of the top row.  Then 
move up and to the right one space (when you run out of squares to 
move to, imagine that your Magic Square were shifted up or over n 
spaces, where n is the dimension of the square) and put a 2 in that square.  

See how I did that above?  Moving up and to the right from 1, I imagined 
that the Magic Square were moved up three spaces, and that's how I knew 
where to put the 2.  Then do the same thing to place the 3.  Keep going 
like this until you reach a space that's already full.  Whe you come to one, 
go back to the space you just came from, and put the next number in the 
space immediately below it. Then continue moving up and to the right, 
and placing the next consecutive numbers, and when you come to a space 
that's already full, deal with it the same way as I just described: go back 
to the space you just came from, and put the next number immediately below it.

If you're having trouble figuring out what I said, look at my example and
see if you can piece it together.  If you're still having trouble, mail us
back.  Have fun!

-Ken "Dr." Math
Associated Topics:
Elementary Projects

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.