Puzzle time! Of colored hats and blindfolded people…
It has been a long time since I posted a puzzle. This is a variation of those category of logic problems where blindfolded people regularly get colored hats put on them and they have to guess the color of the hat on their own head 🙂
This particular one goes this way – Twelve sailors get marooned in an island. The local tribe finds them out and takes them to their leader. Their leader, not knowing what to do with the prisoners, come up with a novel idea. He tells them that next day morning, he was going to line them up in a straight line and put a cap on their head while they are blindfolded. The only colors he has his hats in are black and white. (I do not have the faintest idea why on God’s green earth the tribal leader had black and white hats, but that is what he had 🙂 ) After that, he would remove everybody’s blindfold. Then, every sailor could see the color of the hats of all the people in front of himself but not his own or that of the ones behind.
The leader would start from the last person in the rear and ask him to name the color of the hat he was wearing. He could only say “Black” or “White”. Any other words spoken would result in everybody getting killed. If the person got the right answer, he would be spared, else he would be killed. Then the leader would move to the next person who was ahead of the last person and go thru the same procedure… till he was done with all twelve of them.
You can assume that everybody can hear the answer given by the person being asked. All the people who were spared would be given a boat and shown how to go back to their land.
Tonight, the sailors have to come up with a strategy to save as many of themselves as they can.
What would be the best strategy to maximize the number of people who can survive? How many can survive?