Question 1
Amit says: 'I always tell the truth'
Ravi says: 'Anita is a truth-teller'
Anita says: 'Sometimes I lie, sometimes I tell truth'
Divya says: 'Rahul is a liar'
Rahul says: 'Divya is a truth-teller'
The group has truth-tellers, liars, and one alternator. Who is the alternator?
Identify types by their statements:
- Amit claims to always tell truth. A truth-teller can say this, a liar cannot (would be true statement). So Amit is likely truth-teller.
- Ravi claims 'Anita is truth-teller'. Without knowing Anita's type, this is ambiguous.
- Anita admits to sometimes lying and sometimes telling truth - this is the hallmark of an alternator.
- Divya and Rahul make contradictory claims about each other, suggesting one is truth-teller, one liar.
The key is Anita's self-description. A truth-teller cannot say 'sometimes I lie' (would be false). A liar cannot say 'sometimes I tell truth' (would be true, but liars always lie). Only an alternator can truthfully describe their alternating nature.
Therefore, Anita is the alternator.
- Amit claims to always tell truth. A truth-teller can say this, a liar cannot (would be true statement). So Amit is likely truth-teller.
- Ravi claims 'Anita is truth-teller'. Without knowing Anita's type, this is ambiguous.
- Anita admits to sometimes lying and sometimes telling truth - this is the hallmark of an alternator.
- Divya and Rahul make contradictory claims about each other, suggesting one is truth-teller, one liar.
The key is Anita's self-description. A truth-teller cannot say 'sometimes I lie' (would be false). A liar cannot say 'sometimes I tell truth' (would be true, but liars always lie). Only an alternator can truthfully describe their alternating nature.
Therefore, Anita is the alternator.