A stark raving mad king tells his 100 wisest men he is about to line them up and that he will place either a red or blue hat on each of their heads. Once lined up, they must not communicate amongst themselves. Nor may they attempt to look behind them or remove their own hat.

The king tells the wise men that they will be able to see all the hats in front of them. They will not be able to see the color of their own hat or the hats behind them, although they will be able to hear the answers from all those behind them.

The king will then start with the wise man in the back and ask "what color is your hat?" The wise man will only be allowed to answer "red" or "blue," nothing more. If the answer is incorrect then the wise man will be silently killed. If the answer is correct then the wise man may live but must remain absolutely silent.

The king will then move on to the next wise man and repeat the question.

The king makes it clear that if anyone breaks the rules then all the wise men will die, then allows the wise men to consult before lining them up. The king listens in while the wise men consult each other to make sure they don't devise a plan to cheat. To communicate anything more than their guess of red or blue by coughing or shuffling would be breaking the rules.

What is the maximum number of men they can be guaranteed to save?

100

99
last one is screwed

99 - but how?

Here's the trick - they devise the plan that the last in line will count the blue hats...if there is an odd number then they call out "blue" if there is an even number they call out "red"

99
because if they are in a line the first guy can see the guy in front of hims hat so he knows what color his own hat is..given the king is going blue red blue red..so the rest of the guys in line can see the guys in front of him their hats..but the last guy cant turn around nor does he have someone in front of him to see what color thier hat is so he wont know what color his own hat is ..there for hes screwed and has a 50/50 chance of saying the wtrong color

ok so if you go by your way and the rest get it right because of their little trick does that mean theres still 99 cause the guy calling out the first number has a 50/50 chance to