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

Home > General
Primal Magic Square (Posted on 2004-03-09) Difficulty: 4 of 5
Find a 3x3 magic square that is composed of 9 prime numbers (not the numbers from 1-9) and show how you found it.

(A magic square, as you may already know, is one in which the respective sums of the numbers in all the rows, columns, and both major diagonals all add up to the same number.)

Since "Magic Square" is a term used outside the scope of this problem, I'm sure you can find an answer on the internet. Please find a solution independently.

See The Solution Submitted by SilverKnight    
Rating: 3.0000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re: lower square - failure | Comment 5 of 15 |
(In reply to lower square in progress... by Tristan)

Hmph.  I was brute forcing this using pairs summing up to 90.  After a few failed tries, I thought of a proof of the lack of possibilities there.

Take the two opposite columns.  Their total sum must be 270, because of the three pairs it includes.  Therefore, each row and column must add to 135.  Then, the middle number must be 45, which isn't a prime.

Similarly, the sum of opposite numbers can't be any multiple of ten.

Pushing this further, if the sum of opposite numbers is x, then the sum of each column must be 1.5 * x, and the middle number .5 x.  Therefore, the sum of opposite sides must be double of a prime, and the sum of each row triple of a prime.

I hope this helps others if they happen to be searching the same way I am.

  Posted by Tristan on 2004-03-09 19:32:03
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 (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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