# Colour of Caps

Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.

The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.

They need to guess their own hat colour by writing it on a piece of paper, or they can write ‘pass’.

They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.

If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.

What is the best strategy?

The condition that “*They cannot communicate with each other in any way once the game starts*” makes it impossible to device any strategy whatsoever, because it means that each of them is on his own and answering unaware of anything other than the others’ hats. (This is because writing one’s assumed answer on paper also amounts to “communication” if the answer can be seen by others. )

If the ‘writing own answer’ is NOT counted as ‘communication’, here’s how they can device their strategy:

**Background**: Since there are only two colours and three people, if one person looks at others, there are only three possible sights he can see:

(a) both the others wearing green hat

(b) both of them having blue hat OR

(c) one of them blue and the other, green.

**Strategy**: They decide that:

(a)The first person to answer, say, A, will write answer as follows: If he sees both the others wearing same coloured hat, he will write THAT colour. Otherwise, he will write ‘Pass’.

(b) If A has written a colour, the second person, say, B, knows, from (a), that he himself is wearing that coloured hat. Hence, he will write that colour, and the third person, say, C, also will do the same. (With this, both B and C have answered correctly. Game over. They win.)

(c) If A wrote ‘Pass’, it means that B and C are having different colours. B can see that C is wearing, say, green. Since A’s answer indicate different hat colours for B and C, B can deduce that he (B) must be wearing the other colour, blue (or vice versa). So, he writes ‘Blue’. C also follows the same logic and guesses his hat colour. Game over. They win.

### Your Answer

## More puzzles to try-

### What is the logic behind these ?

3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »### Defective stack of coins puzzle

There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »### Which clock works best?

Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »### (Advanced) Cheryl’s Birthday Puzzle

Paul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »### Five greedy pirates and gold coin distribution Puzzle

Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »### Magical flowers!!

A devotee goes to three temples, temple1, temple2 and temple3 one after the other. In front of each temple, there ...Read More »### Tuesday, Thursday what are other two days staring with T?

Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »### How could only 3 apples left

Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »### How Many Eggs ?

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »### HARD MATHS – How much faster is one train from other Puzzle

Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination ...Read More »### Most Analytical GOOGLE INTERVIEW Question Revealed

Let it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »### Lateral thinking sequence Puzzle

Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »### How did he know?

A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »### Pizza Cost Math Brain Teaser

Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »### Which letter replaces the question mark

Which letter replaces the question markRead More »### Which room is safest puzzle

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »### Richie’s Number System

Richie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »### Srabon wanted to pass

The result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »### Become Normal!!

Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »### Sakib Knows The Number!

Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »