Antimagic Square 4X4

 
 
An antimagic square is an   n \times n   array of integers from  1   to   n^2   such that each row, column, and main diagonal produces a different sum such that these sums form a sequence of consecutive integers.

 

Example #1 :

antimagic-2

Notice that in the above example, the sums contain eight consecutive numbers, namely 32 to 39 inclusive.

 
 
 

Here’s an example of   4 \times 4   anti-magic square containing more than eight consecutive numbers in its sums.
 

 
Example #2 :

 
antimagic-1

 
the sums are   30, 31, 32, 33, 34, 35, 36, 37, 38, 39

Source and explanation:

http://mathworld.wolfram.com/AntimagicSquare.html

 
 

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Advertisements

About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s