Puzzles

A puzzle, especially for mathematicians, and in particular for vbn! In a faraway kingdom, the king had n wise men (let's say 100). The king decided that there were too many wise men:smile18:. He decided to test how wise they really were... He summoned them and said:smile29:, "Tomorrow, you will be lined up in a row (i.e., one after another. The first looks at the wall in front, the second at the first, the third at the second and the first, and so on, the last sees everyone)" and a hat of one of three colors will be placed on each of your heads (randomly - red, blue, or green). And each of you must say what color hat is on your head. If you guess correctly, you live:smile03:, if you guess incorrectly, your head will be chopped off:smile34: :smile05:! A wise man can say only one word! This word is the color of the hat! Question: how many wise men (at most) can 100% survive:smile41:? Clarifications: 1) The wise men will be asked if they want to answer... i.e., the wise men decide when and who to answer. 2) The wise men are willing to sacrifice themselves for the sake of others. If you have any questions, ask... and please send the answer to the puzzle to me in a private message. Good luck! :smile13: P.S. Members of the "Order of the Phoenix" clan, please don't worry... :D to Darth Saruman: this applies to you too... ;)