# Thread: Is there an easy way of doing this?

1. ## Is there an easy way of doing this?

The Jefferson School PTA set up a phone tree in order to reach all of its members. Each person's responsibility, after receiving a call, is to call two other assigned members until all members have been called. Assume that everyone is home and answers the phone, and that each phone call takes 30 seconds. If one of the 210 members makes the first phone call and starts the clock, what is the least amount of time necessary to reach all 210 members of the group?

2. Hello, t-lee!

This one is trickier than I thought . . .

The Jefferson School PTA set up a phone tree in order to reach all of its members.
Each person's responsibility, after receiving a call, is to call two other assigned members
until all members have been called.
Assume that everyone answers the phone immediately, and that each phone call takes 30 seconds.
If one of the 210 members makes the first phone call and starts the clock,
what is the least amount of time necessary to reach all 210 members of the group?

The problem is "small" enough to solve by Brute Force . . .

Member #1 calls member #2 and starts the clock.

Member #2 calls #3 and #4 . . . The two calls take 60 seconds.

#3 and #4 call {5,6,7,8} . . . This takes 60 seconds.

{5,6,7,8} call {9,10,11,12,13,14,15,16} . . . This takes 60 seconds.

{9,10, ... , 16} call {17,18,19, ..., 32} . . . This takes 60 seconds.

{17,18, ..., 32} call {33,34,35, ..., 64} . . . This takes 60 seconds.

{33,34, ..., 64} call {65,66,67, ..., 128} . . . This takes 60 seconds.

{65,66, ..., 113} call {114,115, ..., 210} . . . This takes 60 seconds.

It takes at least 420 seconds = 7 minutes to contact the entire membership.

3. i kind of see were you are coming up with this. is there another way you could show and explain to me? thanks so much for your help. A friend told me that it delt with Fibonacci numbers. but how?