100 logicians were living on a deserted island. One thing peculiar about
them was that they were very against on having black dot on their back. In
fact, if any one of them found out that he had a black dot on his back, he
would commit suicide on that day! However one good thing about them was that
one logician doesn't tell another if he has a black dot or not. So even if a
logician had black dot on his back nobody would tell him, and so he would
never commit suicide!
Thus they were all living merrily, until one
day a visitor came to their island. He stayed with them for a few days, and
then on his last day he gave a farewell speech. In it, he mentioned
something startling to the logicians. He said "How come at least one of you
have a black dot on your back!" This triggered a chain reaction amongst the
logicians. If he hadn't said the last
statement everything would have
been fine. It was found that logician population decreased.
The question is how many logicians committed suicide and how long did it
take (number of days) if there were exactly 5 logicians with a black dot on
their back? Explain your answer.
