A group of 20 people got kidnapped and are held in a cell. The kidnapper tells t

Question

A group of 20 people got kidnapped and are held in a cell. The kidnapper tells them that each of them will be given sleeping pills and at night each will marked on their forehead with a red or black ink dot. Tomorrow, after waking up each one will be able to see all foreheads except one's own but no talking or signalling will be allowed. Then kidnapper will choose the first victim to guess the color of dot. The first victim will say "red" or "black" and will be spared or executed depending on his correct or wrong guess. Then the next victim will be chosen by kidnapper and so on. The problem is that in the remaining evening time before sleeping to come up with a strategy that will guarantee that all will be spared but one who may be spared or may be executed. Describe the strategy.

Explanation / Answer

In case of twenty people if 10 people are marked on their forehead with red dots and 10 with black dots and each guy can see other 19 guys foreheads and in which he can find 10 people having same colour dots and 9 having the other colour and the guy can assume that he belongs to the second group. In this way every student can know the colour of dot marked on their forehead and can be spared.

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