Question 1
Manoj says: 'I always tell the truth'
Divya says: 'Neha is a truth-teller'
Neha says: 'Sometimes I lie, sometimes I tell truth'
Rohan says: 'Vikram is a liar'
Vikram says: 'Rohan is a truth-teller'
The group has truth-tellers, liars, and one alternator. Who is the alternator?
Identify types by their statements:
- Manoj claims to always tell truth. A truth-teller can say this, a liar cannot (would be true statement). So Manoj is likely truth-teller.
- Divya claims 'Neha is truth-teller'. Without knowing Neha's type, this is ambiguous.
- Neha admits to sometimes lying and sometimes telling truth - this is the hallmark of an alternator.
- Rohan and Vikram make contradictory claims about each other, suggesting one is truth-teller, one liar.
The key is Neha'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, Neha is the alternator.
- Manoj claims to always tell truth. A truth-teller can say this, a liar cannot (would be true statement). So Manoj is likely truth-teller.
- Divya claims 'Neha is truth-teller'. Without knowing Neha's type, this is ambiguous.
- Neha admits to sometimes lying and sometimes telling truth - this is the hallmark of an alternator.
- Rohan and Vikram make contradictory claims about each other, suggesting one is truth-teller, one liar.
The key is Neha'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, Neha is the alternator.