Chapter 3.5, Problem 31PS

Consider a silly game called Bluffhead in which each of three players takes a card from a shuffled deck and holds it, face out, to his or her forehead, as shown in the figure.

Undefined term: forehead

Defined terms:

deck of cards

ace, the highest card

Postulates:

1. The player’s names are Alice, Ben, and Cole, who always speak in that order, and then it

goes back to Alice again.

2. Each player makes one of the following statements:

“I win”. (I have a higher card than everyone else.)

“I lose.”(Someone has a higher card than I have.)

“I tie.”(I and at least one other player tie with the highest card.)

“I don’t win.”(I either tie as a winner or lose.)

“I don’t lose.”(I either win or tie as a winner.)

“I don’t’ know.”

3. The players play with perfect logic and reveal information only through acceptable statements.

4.Each player says the strongest thing he or she can – that is, the player chooses the statement that is true and highest on the list.

In Problems 31-36, state what you can infer about the cards from the given statements.

Alice: “I don’t know.”

Ben: “I lose.”

Cole: “I lose.”