Sunday, May 17, 2009

Have you had a wave of head lice going through your child's school, camp or day care? Frustrating and tedious daily combing, nurse calls, parent whisper, days off from school, infinite laundry, empty shampoo shelves at the pharmacy, angry haircuts - all these efforts devoted to fighting a ferocious tiny insect.
How quickly do you think head lice could spread around if we do nothing?
Let's pretend that each day lice spreads from one child to three more. And that lice is smart and populates only "virgin" territories avoiding already infested heads. Say, there are 400 kids at school. And it all starts with a single nit in one child's hair.
How many days would it take for everyone at school to get infested?

P.S. No, we have not had any lice in our neighborhood in the past two years, but swine flu panic was a reminder.

1 comment:

Anonymous said...

Likely, I am bold. So, lice does not bother me.
All 400 kids will get infested on 7th day.
1st day: 1 kid
2nd day: 1 + 3 = 4
3rd day: 1 + 3 + 9 = 13
4th day: 1 + 3 + 9 + 27 = 40
5th day: 1 + 3 + 9 + 27 + 81 = 121
6th day: 1 + 3 + 9 + 27 + 81 + 243 = 364
7th day: 1 + 3 + 9 + 27 + 81 + 243 + 729 > 400

The sequence defining the number of infested on each day: 1, 3, 9, 27, 81, 243, 729 - is geometric progression.
It's sum is:
s = 3^n - 1 / 2
in order to get s > 400
we need n > 6

Michael K.