100 prisoners in jail are standing in a queue facing in one direction. Each prisoner is wearing a hat of color either black or red. A prisoner can see hats of all prisoners in front of him in the queue, but cannot see his hat and hats of prisoners standing behind him.

The jailer is going to ask color of each prisoner’s hat starting from the last prisoner in queue. If a prisoner tells the correct color, then is saved, otherwise executed. **How many prisoners can be saved at most** if they are allowed to discuss a strategy before the jailer starts asking colors of their hats.

Answer:

At-most 99 prisoners can be saved and the 100th prisoner has 50-50 chances of being executed.

The idea is that every prisoner counts number of red hats in front of him.

100th prisoner says red if the number of red hats is even. He may or may not be saved, but he conveys enough information to save 99th prisoner.

The 99’th prisoner decides his answer on the basis of answer of 100’th prisoner’s answer. There are following possibilities and 99’th prisoner can figure out color of his hat in every case.

If 100’th prisoner said ‘Red’ (There must have been even number of red hats in front of him)

a) If 99’th prisoner sees even number of red hats in front of him, then his color is black.

b) If 99’th prisoner sees odd number of red hats in front of him, then his color is red.

If 100’th prisoner said ‘Black’ (There must have been odd number of red hats in front of him)

a) If 99’th prisoner sees even number of red hats in front of him, then his color is Red.

b) If 99’th prisoner sees odd number of red hats in front of him, then his color is Black.

The 98’th prisoner decides his answer on the basis of answer of 99’th prisoner’s answer and uses same logic.

Similarly other prisoners from 97 to 1 are saved.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

## Recommended Posts:

- Puzzle 65 | Hats Off
- Puzzle | 9 Students and Red Black Hats
- Puzzle 51| Cheryl’s Birthday Puzzle and Solution
- Puzzle | 3 Priests and 3 devils Puzzle
- Puzzle 81 | 100 people in a circle with gun puzzle
- Puzzle 85 | Chain Link Puzzle
- Puzzle 15 | (Camel and Banana Puzzle)
- Puzzle 34 | (Prisoner and Policeman Puzzle)
- Puzzle | Elevator Puzzle
- Puzzle 31 | (Minimum cut Puzzle)
- Puzzle 27 | (Hourglasses Puzzle)
- Puzzle 36 | (Matchstick Puzzle)
- Puzzle 39 | (100 coins puzzle)
- Puzzle 28 | (Newspaper Puzzle)
- Puzzle 24 | (10 Coins Puzzle)
- Puzzle 29 | (Car Wheel Puzzle)
- Puzzle 33 | ( Rs 500 Note Puzzle )
- Puzzle 38 | (Tic Tac Toe Puzzle)
- Puzzle | The Pot of Beans
- Puzzle | Who killed him?