Question

If one person sends the e-mail to two friends, asking each of them to copy the
mail and send it to two of their friends, those in turn send it to two of their friends
and so on.
How many e-mails would have been sent by the time it did 30 sets?

Answer 1

2147483646
First person sent the mail to 2 persons. Those 2 sent the mail to 2 persons each,
total 4 persons. Now, those 4 person sent mail to total 8 persons, then 8 to 16
persons, 16 to 32 persons and so on.... Hence, it a series of 2, 4, 8, 16, 32 upto
30 numbers
It is a Geometric series with common ratio 2 and first number is also 2.
Summation of such series is given by A * (Rn - 1) / (R - 1) where
A = First term
R = Common Ratio
n = total numbers
So total number of times mail sent by the time it did 30 sets
= 2 * (230 - 1) / (2 - 1)
= 2 * (1073741824 - 1)
= 2 * 1073741823
= 2147483646