A Hair Raising Problem

Prof John is a very interesting person. We were discussing people's hair. Prof John told me that there are about 150,000 hairs on an average on a man's head. I disagreed with him. I told him that no one could have actually come by this figure - who would have the patience to actually take a man's head and take the hair by hair and count them! 'No' he argued 'It is enough to count them on one square centimetre of a man's head and knowing this and the size of the hair covered surface, one can easily calculate the total number of hairs on a man's head'. Then he popped a question at me. 'It has also been calculated that a man sheds about 3000 hairs a month. Can you tell me the average longevity of each hair on a man's head? Can you guess what my answer was?

The hair that falls last is the one that is the youngest today i.e. the one that is only one day old. Let us now calculate how long it will take before the last hair falls. In the first month a man sheds 3000 hairs out of 150,000 he has on his head. In the first two months 6000. And in the first year 3000 × 12 = 36000 Therefore it will take a little over four years for the last hair to fall. It is in this way that we have determined the average age of human hair.