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## #1 Puzzles and Games » Three Hats Puzzle 100% solution » 2011-11-02 14:19:51

mashplum
Replies: 2

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

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

They need to guess their own hat color 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 \$50,000 each, but if anyone guess incorrectly they all get nothing.

What is the best strategy?

The given solution offers a 75% chance at winning. Here is a 100% method:
Before the game the people agree that if they see a blue and a green hat, they will write pass. If they see a match, they will pause. If everyone pauses, they must all have the same color and they can all safely guess that color. If two people immediately write pass, the third knows to guess the opposite of what the other two are wearing.

## #2 Re: Puzzles and Games » The Monty Hall Problem » 2011-11-02 13:09:47

I love this problem. So many people get it wrong and many who get it right can't explain it. Here is my stab at it:
If your initial choice happened to be the car, then switching would always get you a goat. But if your initial choice was a goat then switching will get you a car. Switching will always get you the opposite of whatever your initial choice was. If you agree with that last statement the solution is obvious. Everyone agrees that your initial choice has only a 1/3 probability of being right and a 2/3 probability of being wrong, so switching would have to be the opposite of that. In other words, would you rather bet that your first choice was a car or bet that it was a goat?

## #3 Re: Puzzles and Games » Four People Travel » 2011-11-02 07:11:49

I am always looking for sites with intelligent puzzles. Invariably, they all have stuff like. Notice that no question is even asked, but we should assume that we are meant to assign a vehicle to each person. We should also expect there to be only one solution. In order for this to be the case, we must read the clues from another point of view and get information that is the opposite of what we would expect. "John gets seasick." could be interpreted as, "John is prone to seasickness and therefore does not go by ship." or it could be interpreted as, "John gets seasick on this particular voyage, therefore he must be on the ship." Similarly, we can assume that Mr. Jones hates flying because he is required to do it all the time, including this trip. That means Rachel is on the train, Cindy is in a rented car, John is unhappily sailing on the ship, and Mr. Jones is not happy about being on the plane. This is the only answer I can find that is remotely satisfying, but it is still a very poor logic puzzle.