A family with three teenagers has just moved into a new home that has a bedroom for each...

A family with three teenagers has just moved into a new home that has a bedroom for each teenager. They decide to use the method of points to decide which room each one gets. Each teenager divides 100 points among the three rooms, and the point assignments are listed in the following table.

a. List the six possible arrangements of teenagers to rooms, and identify the smallest point value assigned to a room in each case.

b. How many arrangements are there for which the smallest number is as large as possible?

c. How should the rooms be assigned to the teenagers?