Suppose Carol from problem 16 wants to change her point assignments. She wants to assign...

Suppose Carol from problem 16 wants to change her point assignments. She wants to assign 20 points to room 1, 40 points to room 2, and 40 points to room 3. The other kids do not want to change their point assignments. Apply the method of points again, using Carol’s new point assignment. How should the rooms be allocated?

Problem 16:

A family with three kids is on vacation. They rent a house, and each kid will have a room of his or her own. It is up to the children to decide who gets which room, so they decide to use the method of points. Each kid divides 100 points between the three rooms, as shown in the following table.

a. List the six possible assignments of kids to rooms and note the smallest point value assigned to a room in each case. How many arrangements are there for which the smallest number is as large as possible?

b. How should the rooms be assigned?