TESTfunda Puzzle of the Week 09-Mar-12

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Testfunda
09-Mar-12
Puzzle of Week
Puzzle #199 - The 100 "Chaturs" (09-Mar-12)
08-Mar-12

People of the Chatur tribe are known for their intelligence and honesty. To test their intelligence, the king of Asgard decides to invite 100 wisest men of the tribe. The process that the king will undertake once the 100 wisest men are in his court is as follows:

The king will write a certain number greater than 1 on their hats and line them up. Once lined up, they will not be allowed to communicate with each other or look behind or remove their respective hats. However, they will be allowed to see the number written on all the hats in front of them. Hence, a person won’t know the number written on his own hat or on the hats behind him. Everyone will be allowed to listen to the answer of every person behind him.

The King, starting from the last man in the queue, will ask each man “Is number written on your hat prime?” The wise men will be allowed to answer “Yes” or “No” only. All men who give the correct answer will dine with the King while the others will be asked to leave the palace silently.

The King makes it clear to the gathered people that if any one breaks any of the rules, then all of them will be severely punished. He allows them to devise their strategy for the game. Assuming that all of them play the game honestly, how many of them will definitely dine with the King? What could be their strategy for the same?

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