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