# Find the minimum number of apples in the carton?

In the world of fruits and shares, a carton of apples becomes the center of a mathematical puzzle. Divided into equal parts and distributed among traders, the apples take a fascinating journey leading to a perplexing question about the minimum number of apples in the carton. Let's uncover the mystery behind this intriguing math problem.

A carton contains some apples which were divided into two equal parts and sold to 2 traders Tarun and Tanmay. Tarun had two fruit shops and decided to sell an equal number of apples on both shops A and B respectively. Tanya visited shop A and bought all the apples in the shop for her kids. But one apple was left after dividing all the apples among her children. Each child got one apple, find the minimum number of apples in the carton?

**Answer: Minimum of 12 apples**

**Explanation : **

Let the number of children be X,

Therefore, the number of apples bought by Tanya = ( X + 1)

The total number of apples in the shop A = ( X + 1)

Total number of apples bought by Trader Tarun = 2( X + 1 )

Total number of apples in the carton = 4( X + 1 )

Now, the minimum no. of apples in a carton:

We assume: X is not equal to 0

X is not equal to 1 ( Tanya has children not a single child)

X equal to 2 (Tanya has a minimum of 2 children)

When X = 2

Let the number of children be X

Therefore, the number of apples bought by Tanya = ( X + 1)

The total number of apples in the shop A = ( X + 1)

Total number of apples bought by Trader Tarun = 2( X + 1 )

Total number of apples in the carton = 4( X + 1 )

Now, minimum no of apples in carton:

We assume:

X is not equal to 0

X is not equal to 1 ( Tanya has children not a single child)

X equal to 2 (Tanya has a minimum of 2 children)

When X = 2

4( X + 1 )

= 4( 2 + 1 )

= 12

Thus, minimum of 12 apples

Through a logical sequence of divisions and considerations, we've discovered that the minimum number of apples in the carton is $4$. This mathematical puzzle demonstrates the intricacies of fair division and the surprising outcomes that emerge from seemingly straightforward transactions in a fruit distribution scenario.