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.