
WASHINGTON STATE MATHEMATICS COUNCIL 2001 MIDDLE SCHOOL MATH OLYMPIAD Session I: FIFTH/SIXTH GRADE PROBLEM SOLVING 
56 
Phone Tree
In
case of an emergency radiation leak at a nearby nuclear power plant, the
manager is setting up a phone tree to call 10,000 homes in 15 minutes. In round
1, the manager calls 3 homes. In round 2, the person called in each of the 3
homes calls 3 more homes, who then each call 3 additional homes, and so on
until all 10,000 homes have been called. This is called a 3person phone tree. The
manager starts calling at 10:21 and the phone tree must reach all homes in 15
minutes.
A
community member is concerned that this may take too long and proposes a
5person phone tree. The manager would call 5 homes and each person in turn
would call 5 more homes and so on. The
community leaders want to know:
1.
Will
the 3person phone tree work for the current 10,000 homes?
2.
Will
the 3person phone tree work for a future population of 50,000 homes?
3.
Will
the 5person phone tree be needed now (with 10,000 homes) or in the future
(with 50,000 homes)?
1.
Table or
Diagram: For each of the two proposed plans,
draw a table or diagram showing how many rounds of calls must be made before
all homes are contacted, and explain
how you came up with the figures. You
need to figure out how many calls, total,
have been made at the end of each round.
·
Assume that the
manager starts the first call at 10:21 am.
·
Assume that each call
lasts 1 minute, including dialing time.
·
Assume that the next
round of phone calls does not begin until all homes have been contacted during
the current round.
2.
Exact Time
Needed for Each Plan: For each of the two proposed plans, you must
state exactly how long it will take to reach all the homes.
Prepare a report for the community leaders. In this report you
must:
·
State your
understanding of your assignment.
·
Summarize your
findings about the two proposed plans for contacting the current 10,000 homes
and the possible future plan for 50,000 homes.
·
State your
recommendation: Should they use a 3person tree? Should they use a 5person tree?
What is your recommendation for this community? Give your reasons for your recommendation.
·
Your Answer(s).
·
Your Understanding of
the Problem.
·
Your Strategies Used.
·
Your Communication.
·
Your
Reasonableness/Reasoning.