Concept explainers
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.”
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Nature of Mathematics (MindTap Course List)
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education