1000 Coins and 10 Bags | Puzzles for Interview - Interview Preparation PDF Download

Introduction

A dealer has 1000 coins and 10 bags. He has to divide the coins over the ten bags so that he can make any number of coins simply by handing over a few bags. How must divide his money into the ten bags?

Method

To solve this puzzle, we can represent each bag as each place value which takes either the value of 0 or 1. For example, if we have to give 7 coins then it is represented as 0000000111. The last 3 digits of 1 represent that those 3 bags whose place values are 1,2,4 are to be given to give 7 coins. Remember that each bag should be either given or not given, which means there are only 2 choices available, which has similarity with the numbers in base 2 where each digit has only 2 values either 1 or 0.

Steps

We can fill coins in the 10 bags in increasing order of 2^n where n varies from 0 – 8, filling the last bag with all remaining coins as follows:

1 = 2⁰ = 1
2 = 2¹ = 2
3 = 2² = 4
4 = 2³ = 8
5 = 2⁴ = 16
6 = 2⁵ = 32
7 = 2⁶ = 64
8 = 2⁷ = 128
9 = 2⁸ = 256
10 = remaining coins = 489

Conclusion

Now, the dealer can make any number of coins just by handing over the bags. For example, if the dealer needs to give 519 coins, it can be represented as bag 2 + bag 4 + bag 8 + bag 16 + bag 489. By following this method, the dealer can easily divide 1000 coins into 10 bags and make any number of coins by handing over a few bags.