A man has sent a message to four of his friends, and each of them has sent the same message to another four friends and so on. Given that each person has received the message only once, determine how many people got the message in the sixth time.
Initially, the message was received by one person (i.e., ).
Then on each iteration, every person who has received the message sends it to four people.
We express this mathematically as follows: . Consequently,
Hence, we can express the iteration as .
Therefore, on the sixth iteration, the number of people who received the message is