## Puzzle #60: Hats and Survival

I just heard this puzzle 15 minutes back at Alok Mittal’s Mathematical Circles where he gave this puzzle to all the children. Great puzzle – will encourage all children as well as adults to try this.

There is an unlimited supply of red and black hats, out of which, at random, 3 hats are pulled out and placed on the heads of three prisonersÂ (call them A, B and C). All of them can see each other (and of course the hat color on top of the other folks), but cannot see themselves. At one simultaneous instant, all three of them are supposed to guess the color of their hat, and they are allowed three answers – Red, Black and Pass. Pass does not count as a correct answer, but is not a wrong answer either. All three of them are now allowed to say a Pass.

If there is anyone who gives a wrong answer, then all of them will be killed. If no one is wrong, and at least one is right, then they will all be set free. They are allowed to discuss their strategy before this event occurs. What should their answering strategy to maximize the chances of survival.

As an illustration, if all of them decide to guess Red, then the chances of survival are 12.5% as all of them being Red has a probability of 12.5%.

As always, please send your answers directly to me at alokgoyal_2001@yahoo.com. If you like the puzzle, please share it with others. If you have interesting puzzles to share, please send them to me at my e-mail given above.

Happy strategizing!

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