"In an ancient village, there were some green-eyed and b lue-eyed persons. One fine day, God instructed them, "th e day on which you come to know that you are a green-ey i, you should commit suicide . hat there was at least one green-eyed among them. Well. all the villagers were very intelligent and strict foll Owers of God. But, hey didn't have mirrors. They couldn" t even communicate with each other. Al1 that they could do is to see colou r of other's eyes. It happened that on 20th day, all the green-eyed people committed suicide. So, how many green eyed were there ?
Answers
Answer:
Step-by-step explanation:
Please make it simple
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if there were n greens to start with, they would leave on the n-th day.
proof by induction:
n=1: If there was one green only, he would see that the rest are blue and he would know that the he must be the green one that god promised. so he would leave on the 1st day.
Suppose true for n=k.
n=k+1: Each one of the k+1 greens would see k other greens. They would each hope that they themselves are blue. So if they truly were blue, they would think that the village had k greens. So they would each expect all the greens to leave by the k-th day (because we suppose that the claim is true for n=k). But the k-th day would come and go and nobody would leave. So each of the k+1 greens would realize that they're green and so would leave the very next day- the (k+1) th day.
so, 20th day =(K+1) th day
so, 20 green eyed were there.