A family with three kids is on vacation. They rent a house, and each kid will have a roo...

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?