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20. Magic Square

Shown below is a magic square where rows, columns and diagonals have the same total. Can you find the value of x?

 

Scroll down the page for the answer.


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

labelling the square as follows we have

if the total is t then, from column 1:

t = 18 + x

using the 2nd row:

5 + p + 15 = 18 + x
so p = x - 2

and using the bottom left to top right diagonal:

x + (x - 2) + q = 18 + x
so q = 20 - x

using the third column:

(20 - x) + 15 + r = 18 + x
so r = 2x - 17

and using the top left to bottom right diagonal:

13 + (x - 2) + (2x - 17) = 18 + x
so x = 12

and the other missing entries can now be calculated and the complete square is shown below:


 

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