The following problems use the last-diminisher method of fair division. Six people will...

The following problems use the last-diminisher method of fair division.

Six people will use the last-diminisher method to divide a cake. Player 1 will begin and will cut a piece that is valued at one-sixth of the entire cake. Each player will decide, in turn, whether to trim the slice. The following table lists the players who trim the cake in each round.

a. Which players are left after round 1?

b. Who cut the piece of cake in round 3?

c. List the players who keep the slice in rounds 1, 2, 3, and 4.

d. Who are the last two remaining players, and how will they fairly divide the remaining cake?