In a remote town where the internet has not yet reached, people use a indigenous telephone to communicate.
Each telephone call occupies the phone to the nearest minute ceiling. So if a call is 15 seconds long, it will be considered a 1 minute call. If it is 3 minute 2 seconds it will be a 4 minute call.
The telephone company charges 1 cent for the first minute, 2 for the second and so on.
One fine Saturday morning at 0900 hours, the Mayor's wife phones two close friends inviting them to an event the coming Monday at 6:00 pm.
The invite is to be forwarded to at least 1 and maximum of 3 other town residents via telephone. Each invite takes the same time in minutes as the invitee number.
Assuming there are no multiple invites the questions are :
1) What would be the minimum time taken to reach 50000 unique residents in the town? How much money would the telephone company have made in this case?
2) How many maximum invites could have been reached in the first three hours?
3) With above conditions What would be the strategy be to reach the maximum but get charged the minimum in the first three hours?