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

Home > Numbers
Prime magic (Posted on 2018-09-29) Difficulty: 2 of 5
What is the smallest possible constant of a 3×3 magic square containing nine distinct non-composite numbers only?

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
solution(?) | Comment 2 of 3 |
As Steven pointed out below, non-composite does not mean the values have to be positive. As all negative numbers are not, by definition, composite, nor are 0 or 1, the smallest possible constant would wind up being zero

-2 -1 3
5 0 -5
-3 1 2

The above square is 9 distinct terms, none of which are composite, which fits the requirements set forth by the problem.

If we instead hold to primes, as the problem title suggests, allowing no negative terms, the smallest constant would be 177

17 89 71
113 59 5
47 29 101

Finally, if we allow 0 and 1, but still no negative values, our smallest constant becomes 111

7 61 43
73 37 1
31 13 67



  Posted by Justin on 2018-09-29 16:11:21
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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