### Brain Teasers

# E-mails

Mad Ade sends an e-mail to two friends, asking each of them to copy the e-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 30 sets of e-mails had been forwarded?

How many e-mails would have been sent by the time 30 sets of e-mails had been forwarded?

### Answer

2147483646Mad Ade 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 a total of 8 persons, then 8 to 16 persons, 16 to 32 persons and so on.... Hence, it a series of 2, 4, 8, 16, 32 up to 30 numbers.

It is a geometric series with a 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 30 sets of e-mails had been forwarded

= 2 * (2^30 - 1) / (2 - 1)

= 2 * (1073741824 - 1)

= 2 * 1073741823

= 2147483646

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