Question

A remote island has a unique social structure. Individuals are either "Truth-tellers" (who always speak the truth) or "Tricksters" (who always lie). You encounter three inhabitants: X, Y, and Z. 

X says: "Y is a Trickster" 
Y says: "Exactly one of us is a Truth-teller." 
What can you definitively conclude about Z?

• A. Z could be either a Truth-teller or a Trickster
• B. Z is a Trickster
• C. Z is a Truth-teller
• D. The information is insufficient to determine Z's identity

Hint:

When dealing with logic puzzles involving truth-tellers and liars, work through each possible case and consider the truth of statements made by others to determine the possible identities.

Answer 1

The Correct Option is A

We are given the following statements:
- X says: "Y is a Trickster."
- Y says: "Exactly one of us is a Truth-teller."
Let's consider the possible cases:
1. Case 1: If X is a Truth-teller:
- If X is a Truth-teller, then X's statement is true, so Y must be a Trickster.
- If Y is a Trickster, then Y's statement "Exactly one of us is a Truth-teller" must be a lie, meaning that both X and Z are either both Truth-tellers or both Tricksters.
- Therefore, Z must also be a Trickster.
2. Case 2: If X is a Trickster:
- If X is a Trickster, then X's statement "Y is a Trickster" is false, meaning that Y must be a Truth-teller.
- If Y is a Truth-teller, then Y's statement "Exactly one of us is a Truth-teller" must be true, meaning that X and Z must both be Tricksters.
In both cases, we conclude that Z could either be a Truth-teller or a Trickster, so we cannot definitively determine Z's identity based on the given statements.
Thus, the correct answer is option (a).