Chapter 3, Problem 35E

Exercise 35 through 38 refer to the following situation: Angela, Boris, and Carlos are dividing the vanilla-strawberry cake shown in Fig.3-23(a) using the lone-chooser method. Fig.3-23(b) shows how each player values each half of the cake. In your answers assume that all cuts are normal “cake cuts” from the center to the edge of the cake. You can describe each piece of cake by giving the angles of the vanilla and strawberry parts, as in “ $15°$ strawberry- $40°$ vanilla” or “ $60°$ vanilla only.”

Suppose that Angela and Boris are the dividers and Carlos is the chooser. In the first division, Boris cuts the cake vertically through the center as shown in Fig.3-24, with Angela choosing $s_1$ (the left half) and Boris $s_2$ (the right half). In the second division, Angela subdivides $s_1$ into three pieces Boris subdivides $s_2$ into three pieces.

a. Describe how Angela would subdivide $s_1$ into three pieces.

b. Describe how Boris would subdivide $s_2$ into three pieces.

c. Based on the subdivisions in (a) and (b), describe a possible final fair division of the cake.

d. For the final fair division you described in (c), find the value (in dollars and cents) of each share in the eyes of the player receiving it.