Question

Find out the missing number of the magic square.

17		11
	14
17		11

Answer 1

Hint: In magic square, the sum of rows, column and diagonal remains the same.

Complete step by step answer:
(1) Calculate sum of diagonal first as all its terms are known
\[17 + 14 + 11 = 42\]

 (2) Let $x$ be the value in first rows

17	\[(x)\,\]	11
	14
17		11

\[
  \therefore \,x + 17 + 11 = 42 \\
  x + 28 = 42 \\
  x = 42 - 28 \\
  x = 14 \\
 \]

(3) Now, let y be the missing value in the 1st column.

17	14	11
\[(y)\,\]	14
17		11

\[
  \therefore 17 + y + 17 = 42 \\
   \Rightarrow 34 + y = 42 \\
   \Rightarrow y = 42 - 34 \\
  y = 8 \\
 \]

(4) Now, let $z$ be the missing value in third row

17	14	11
8	14
17	\[(z)\,\]	11

\[
  \therefore \,17 + z + 11 = 42 \\
   \Rightarrow 28 + z = 42 \\
   \Rightarrow \,z = 42 - 28 \\
  z = 14 \\
 \]

17	14	11
8	14
17	14	11

(5) Now, let $t$ be the missing value in the 3rd column.

17	14	11
8	14	\[(t)\,\]
17	14	11

\[
  \therefore 11 + t + 11 = 42 \\
   \Rightarrow t + 22 = 42 \\
   \Rightarrow t = 42 - 22 \\
  t = 20 \\
 \]
This is the required magic square.

Note: To find the length of the diagonal of a square, multiply the length of one side by the square root of $2$, if the length of one side is $x$. The diagonals of a square intersect (cross) at \[90\] degree angle, this means that the diagonals of the square are perpendicular.