Magic Square Puzzle

On 4th April 2016, we brought you another math brainteaser. This edition of Monday Brainteaser had you wrapping your mind around finding the missing numbers in a magic square.

Math Brain Teaser

Brainteaser Monday 4416

 

So, were you able to crack it?

Don’t worry if you were not. We have solved it for you.

The Solution

In order to solve this brainteaser, one should know what is a magic square.

A magic square is an n x n (square) matrix wherein numbers from 1 to nare arranged so that each number occur once, and such that the sum of any row, any column, or any main diagonal is the same. Also, one more point to note is that this sum is always equal to n(n2 + 1)/2.

Pretty tricky isn’t it?

But the puzzle presented above is a very simple one. If you look keenly, you might be saved from the mumbo-jumbo of solving a complex equation.

The magic square has all the numbers present in one diagonal.  13, 11, 6, 4. On adding the 4 we get to know that each row and column will have to total to 34.

Next, we take up either the rows or the columns and go about finding the missing number.

Row 1

w + 3 + 2 + 13 = 34

w + 18 = 34

w = 34 – 18

w = 16

Row 2

5 + x + 11 + 8 = 34

x + 24 = 34

x = 34 -24

x = 10

Row 3

9 + 6 + y + 12 = 34

y + 27 = 34

y = 34 – 27

y = 7

Row 4

4 + 15 + 14 + z = 34

33 + z = 34

z = 34 – 33

z = 1

And here is the final magic square matrix

Magic Square