The following is the puzzle that I am trying to figure out. I know the "expected solution of 99". But honestly, I think this puzzle is flawed. How exactly can each wise man know the number of hats saved if they died silently? Doesn't make sense to me.
A stark raving mad king tells his 100 wisest men he is about to line them up and place either a red or blue hat on each head. Once lined up, they must not communicate amongst themselves nor attempt to look behind them nor 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.
Before they are lined up, the king makes it clear that if anyone breaks the rules then all the wise men will die. The king listens in while the wise men consult each other to make sure they don't devise a plan to communicate anything more than their guess of red or blue.
What is the maximum number of men they can be guaranteed to save?