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 email@example.com)
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.