Question

Find the missing number in the given puzzle.
8 13
6 6
4 19
22 2
? 32

Answer 1

Hint:
Here, we need to find the missing number. We will find a relation of the numbers in the left column and the right column of numbers, such as sum, difference, multiple, etc., and use that relation to find the missing number. The missing number should follow the same relation with the number 32.

Complete step by step solution:
Let the column with the numbers 8, 16, 4, 22, and the missing number be column A.
Let the column with the numbers 13, 6, 19, 2, 32 be column B.
We need to find a relation between the corresponding numbers in column A and column B. The relation can include any arithmetic operation.
First, we observe the difference between the first numbers in column B and column A.
\[13 - 8 = 5\]
Similarly, we observe the difference between the second, third, fourth numbers in column B and column A.
\[\begin{array}{l}6 - 16 = - 10\\19 - 4 = 15\\2 - 22 = - 20\end{array}\]
We can see that there is a pattern in these equations.
The difference of the first numbers is the first multiple of 5, with the positive sign.
The difference of second numbers is the second multiple of 5, with the negative sign.
The difference of third numbers is the third multiple of 5, with the positive sign.
The difference of fourth numbers is the fourth multiple of 5, with the negative sign.
Therefore, the difference of the fifth numbers must be the fifth multiple of 5, with the positive sign.
We can write this in form of an equation as
\[32 - ? = 25\]
Simplifying this equation to find the missing number, we get
\[? = 7\]

\[\therefore\] The missing number is 7.

Note:
We can also find some other relation and get a different value for the missing number. It will be correct as long as the relation is true for all given numbers. For example, we can observe the sum of the two numbers.
\[\begin{array}{l}8 + 13 = 21\\16 + 6 = 22\\4 + 19 = 23\\22 + 2 = 24\end{array}\]
You can observe that the sum of numbers forms a sequence 21, 22, 23 and 24. Thus, the sum of the fifth numbers in the two columns should be 25.
\[\begin{array}{l}? + 32 = 25\\? = - 7\end{array}\]
Therefore, the value of the missing number can also be \[ - 7\]. However, this answer will not be correct if the question states that the missing number is a positive number.