There are a group of 10 people travelling on a certain journey. On the way they come across a dense forest which they need to cross. After a lot of consideration they finally decide to go on the move. But unfortunately on the way they get trapped by a witch, who gets them all tied-up and bound. Now they try to please the witch in every way possible to save their skin.
Finally the witch agrees to a certain condition. Here goes the condition:
The witch had an infinite number of red and blue caps with her. So she decides to get them standing in a row, facing the same direction and placing a cap on each of their head (the cap could be of any color either blue or red). Now each of them has to guess the color of the cap on their head starting from the guy standing at the end of the row. If he is right he would be spared of his life else he would be killed by the witch. The only saving grace was, they were given a chance to decide a strategy which would enable the maximum number of the group to save their lives.
What do you think the optimum strategy should be which could save the maximum number of them and how many will that be?
Note: You can assume the group functions as a whole and each one has an altruistic behavior wherein they think of the benefit of the whole group rather than their own.
You can also assume, what one person speaks is audible to the rest of the group.
Each of the men are given only a single chance to guess the color of the cap on his head.
They are not supposed to do anything else other than just speak out the color - 'just one word'.
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