Puzzle: Another encounter with Illogical Club

Submissions to this puzzle are due by 6:00pm on Thursday, April 16.
EC Math Club is hosting a games night at 6:30pm on Thursday. At that event, we will hand out prizes for the year-long standings in POTW. Come to claim your prize and play some games!
(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. They also know who is not  a member of Logic Club (e.g. who is a member of Illogical Club).

Members of Illogical Club sometimes tell lies and sometimes tell truths. It depends on their mood! (However, members of Illogical Club do happen to know which members of Logic Club are Truthers and which are Liars; they may just choose to tell lies or truths about their knowledge.)

You attend a campus event and bump into three people. In general, you may have to determine which club someone belongs to, based on their statements. However, for this puzzle, you happen to know that there is exactly one Illogical Club member, exactly one Logical Truther, and exactly one Logical Liar in your midst.

• X says: "I am in Logic Club and I am a Truther."
• Y says: "I am in Logic Club and I am a Liar."
• Z says: "Y is in Illogical Club."

Who is the Logical Truther, who is the Logical Liar, and who is the Illogician?

Note: A correct answer is good, but an explanation is better.

Puzzle: First encounter with Illogical Club

Submissions to this puzzle are due by midnight on Sunday April 12.
(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.

Members of Illogical Club sometimes tell lies and sometimes tell truths. It depends on their mood! (However, members of Illogical Club do happen to know which members of Logic Club are Truthers and which are Liars; they may just choose to tell lies or truths about their knowledge.)

(In this first encounter with Illogical Club, you know who belongs to which club. In the future, you may have to determine which club someone belongs to, based on their statements!)

You attend a campus-wide recruitment fair. There, you find a table for Logic Club attended to by two members thereof: Larry and Linda.

Next to them is a table for Illogical Club, attended to by a sole member thereof: Igor.

You approach the two tables and, unprovoked, the club members speak to you:

• Igor says: "Larry is a Truther."
• Larry says: "If what Igor just said is a truth, then Linda is a Liar."
• Linda says: "What Igor just said is a lie."

What are the roles of these Logic Club members, and why? Is Igor's statement a truth or a lie?

Note: A correct answer is good, but an explanation is better.

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.

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?

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?