Five people, Abe, Beth, Cathy, Donna, and Eric, will share a cake using the last-diminis...

Five people, Abe, Beth, Cathy, Donna, and Eric, will share a cake using the last-diminisher method. The people will take turns evaluating and possibly trimming the pieces, in alphabetical order. Consider each of the following scenarios.

a. Abe cuts the first slice. Describe what would have to happen in this round in order for Donna to keep that slice.

b. Abe cuts the first slice. Beth and Cathy each trim the piece, but neither Donna nor Eric trims the piece. Who keeps the piece of cake, and who cuts a slice of cake in the second round?

c. In the second round, one of the players will cut a slice of cake. What value will this player place on the slice?

d. The following table shows who trimmed the slice during each round. For each round, tell who cut the piece and who ended up keeping the piece.