Monday, March 30, 2015

Puzzle: Logic Club and a "hire power"

Submissions to this puzzle are due by midnight on Monday April 6.
(See sidebar for submission rules: email sullivanb@emmanuel.edu)

To join Logic Club, you must decide to always tell the truth or always lie. Members of Logic Club know who among them are Liars and who are Truthers, and they always follow the rules according to their role.

You happen to be in attendance at a communal interview with three candidates for teaching positions at Emmanuel College, and the school needs your help! It is known that these three candidates (inventively named A, B, and C) are members of Logic Club, but it is not (yet!) known what their roles are. The school would only like to hire a Truther. Your goal is to figure out which of the three candidates is a Truther.

  • A says: "If B is a Liar, then C is a Liar."
  • B says: "If C is a Liar, then A is a Liar."
  • C says: "A is a Liar and B is a Liar."
Who should be hired? Which candidate is a Truther, and why?
Note: A correct answer is good, but an explanation is better.

Monday, March 23, 2015

Puzzle: Another encounter with Logic Club

Submissions to this puzzle are due by midnight on Sunday March 29.

(See sidebar for submission rules: email sullivanb@emmanuel.edu)

To join Logic Club, you must decide to always tell the truth or always lie. Members of Logic Club know who among them are Liars and who are Truthers, and they always follow the rules according to their role.

It just so happens that the Math Department faculty are members of Logic Club! You're on your way to find Ben, and you bump into Todd and Patterson standing outside Ben's office.

  • You ask them both: "Is Ben in his office now?"
  • Todd replies: "Ben is here and Ben is a Liar."
  • Patterson replies: "Ben isn't here and Ben is a Liar."
  • At that moment, Ben pokes his head out of his office and says: "Hey, I heard you guys! Todd is a Liar!"
  • Paterson chimes in again: "Yeah, that's right; Todd is a Liar."

What are the roles of Todd, Patterson, and Ben?
Which are Truthers and which are Liars?

Friday, March 20, 2015

Puzzle: An encounter with Logic Club

Submissions to this puzzle are due by midnight on Sunday March 22.

(See sidebar for submission rules: email sullivanb@emmanuel.edu)

To join Logic Club, you must decide to always tell the truth or always lie. Members of Logic Club know who among them are Liars and who are Truthers, and they always follow the rules according to their role.

It just so happens that the Math Department faculty are members of Logic Club! You meet three of them -- Yulia, Brendan, and Christine -- in the hallway one day and decide that you want to determine each of their roles, Truther or Liar.
  • You ask Yulia: "What is your role in Logic Club?"
  • She answers in Russian, so you cannot understand!
  • You turn to Brendan and ask: "What did Yulia say?"
    Brendan replies: "Oh, she just said that she is a Liar."
  • Yulia chimes in (in English) to say: "That's correct."
  • But Christine jumps in to say: "Wait, don't believe them; they're both Liars!"
What are the roles of Yulia, Brendan, and Christine?
Which are Truthers and which are Liars?