Question

A chain email starts with a person sending an email out to five others. Each person who receives the email is asked to send it on to five other people. Some people do this, but others do not send any emails.

a) How many people have seen the email, including the first person, if no one receives more than one email and if the chain email ends after there have been one hundred people who read it but did not sent it out?

b) How many people sent out the email?

I'm supposed to use a tree to solve this problem

Answer 1

Solution

Since every person either sends the email to five other people or does not send the email,a vertex is either an internal vertex with 5 children or is a no internal vertex (Definition: A full m-ary tree where every internal vertex has exactly m children).

By theorem,Which states that ,A full m-ary tree with i internal vertices contains n=mi+1 vertices.

This implies that the tree forms a full 5-ary tree.ie.., m=5

Since 100 people send out the email, there are 100 internal vertices.ie.., i=100

Using the above theorem,the number of vertices is ,

n=mi+1=5*100+1=500+1=501

Thus there are then 501 people who received the email.

100 of the 501 people send out email,thus 501-100=401 people did not send out the email.

a)

501 people received the email.

b)

401 people did not send out the email.