[HELP]

1. For doing the interior decorations of my apartment, I have bought a
roll of roofing paper. I do not know its exact thitkness, but let us
assume it is X. How can I find out how long the roll is without
unrolling it? In other words, can you derive a formula for length of
roll if the radius is r?



2. The numbers 220 and 284 are known as amicable numbers. The reason is
the sum of the proper divisions of220 equals 284 and what is even more
interesting is the sum of the proper divisors of 284 equals 220. $0 far
about 100 pairs of amicable numbers are known. Can you find some in
four digits?



3. Vikram Chadda has two children, and at least one of them is a girl. What is the probability that both children. are girls?



4. In India water lillies grow extremely rapidly in the ponds. If the
growth enlarged so much that each day it covered a surface double
that which it filled the day before, so that at the end of the
20th day if entirely covered the pond, in which it grew, how long
would it take two water lillies Qf the same size at the outset
and at the same rate of growth to cover the same pond?



5.You were to count one number per second and counted seven hours per day, how long would it tcike you to count to a Billion?