# Three Hat Puzzle

As three people enter a room, a hat is placed on each head.

The color of each hat (red or blue) is determined by a coin toss.

Each can see the other hats, but not his own.

They are not allowed to communicate once the game begins.

After looking at the other hats, all must simultaneously guess the color of their own hats or pass.

The group shares a big prize if at least one guesses correctly and none guess incorrectly.

For example, if one guesses “Red” and others “pass” gives 50% chance.

**What strategy should the three agree on to maximize their chances?**

**Solution:**

If you see 2 red hats, then guess that yours is blue.

If you see 2 blue hats, then guess that yours is red.

Otherwise, you see one red and one blue, then pass.

Your team of 3 will only fail if all hats are red or all are blue.

You lose 2 out of 8 possible outcomes, your chances of winning are 75%.