Question 1
Neha (father) says: 'Sunil is a liar'
Sunil (mother) says: 'Vikram is a liar'
Vikram (son) says: 'Amit is a liar'
Amit (daughter) says: 'Neha is a liar'
Exactly two family members tell the truth. Who are the truth-tellers?
This is a classic cycle puzzle.
With an even number of people (4) in a cycle of accusations,
the unique solution is that alternating people are truth-tellers.
Therefore:
Neha (father) = Truth-teller
Sunil (mother) = Liar
Vikram (son) = Truth-teller
Amit (daughter) = Liar
Verification:
Father (T) says 'Mother is liar' - TRUE ✓
Mother (L) says 'Son is liar' - FALSE (son is T) ✓
Son (T) says 'Daughter is liar' - TRUE ✓
Daughter (L) says 'Father is liar' - FALSE (father is T) ✓
This is the unique consistent assignment.
With an even number of people (4) in a cycle of accusations,
the unique solution is that alternating people are truth-tellers.
Therefore:
Neha (father) = Truth-teller
Sunil (mother) = Liar
Vikram (son) = Truth-teller
Amit (daughter) = Liar
Verification:
Father (T) says 'Mother is liar' - TRUE ✓
Mother (L) says 'Son is liar' - FALSE (son is T) ✓
Son (T) says 'Daughter is liar' - TRUE ✓
Daughter (L) says 'Father is liar' - FALSE (father is T) ✓
This is the unique consistent assignment.