Gem in Pockets | Puzzles for Interview - Interview Preparation PDF Download

Introduction

Vijay Dinanath Chauhan, also known as "VDC," was traveling with his friends from Bangalore to New Delhi. He had some Cadbury gems in his cargo jeans pockets, and he planned to give them away to beggars when he arrived in Delhi. Unfortunately, he lost one packet of gems on the way.

Problem

VDC wanted to distribute the gems equally among the beggars, but he didn't know how many beggars there were. He needed to figure out the number of beggars so that he could divide the gems equally.

Solution

To solve the problem, we need to use some math. Let's call the number of pockets in VDC's jeans N. We know that there are N packets of gems, and each packet has N gems. So, the total number of gems is N*N*N-(N) because he lost one packet.
This expression can be simplified to N(N^2-1). We need to find a number that is divisible by 6 because VDC wants to distribute the gems equally. To do this, we can substitute different values of N into the expression.
When N is 2, the expression is 2(2^2-1) = 6, which is divisible by 6. When N is 3, the expression is 3(3^2-1) = 24, which is also divisible by 6. When N is 4, the expression is 4(4^2-1) = 60, which is also divisible by 6.
We can continue this pattern, and we will find that all values of N that are greater than 1 will give us a number that is divisible by 6. Therefore, the number of beggars can be any even number greater than or equal to 2.

Conclusion

In conclusion, VDC could have eaten the gems any other day, but he wanted to give them away to the beggars. To distribute the gems equally, he needed to know the number of beggars. Using some math, we found that the number of beggars can be any even number greater than or equal to 2.