Guess Color of Hat | Puzzles for Interview - Interview Preparation PDF Download

Introduction

In this puzzle, there are 20 people standing in a line, each wearing a hat of either black or white color. The objective is for the group to guess the color of their own hat correctly. But there is a catch, each person can only see the hat of the people standing ahead of them in the line, not behind them. So, what can be the best strategy to guess the color of the hat correctly?

Strategy

Before starting the exercise, the group can discuss and form a strategy. The person standing last in the queue will count the number of white hats on the heads of the 19 people present ahead of him. If this number is even, he will guess the hat on his head as ‘Black’. If the number is odd, he will guess ‘White’. However, the probability of his guess being correct is only 50%.

The Guess as a Message

The guess of the last person functions as a message to others in front of him. Suppose the 20th person guesses ‘Black’. Now, the person who is 19th in the queue knows that the number of white hats on the first 19 people (the 18 people in front of him and himself) is even. He then checks whether the number of white hats in front of him is even or odd. If the number is even, that means the hat on his head is black. If the number is odd, that means the hat on his head is white and calls that out (loudly). Therefore, the 19th person in the queue always guesses correctly, based on the message the 20th person passed on.

Similar Strategy for Others

A similar strategy is followed by each person in turn. Therefore, everyone except the last (20th) person guesses correctly for sure. The answer to this puzzle, therefore, is 19.

Conclusion

In this way, by using a simple strategy, the group can guess the color of their hat correctly with a maximum number of correct guesses.