Question 1
Sunil says: 'Amit took the crystal'
Amit says: 'I did not take the crystal'
Anita says: 'Sunil is a truth-teller'
Sunil says: 'Exactly one of us took the crystal'
Who took the crystal?
Step 1: If Sunil is truth-teller, then:
- Amit took the crystal (from statement 1).
- Exactly one person took the item (from statement 4).
- Amit says 'I did not take it' - FALSE, so Amit is liar (consistent).
- Anita says 'Sunil is truth-teller' - TRUE, so Anita is truth-teller.
This gives: Sunil=T, Amit=L, Anita=T with Amit as thief.
Step 2: If Sunil is liar, then:
- Amit did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Amit didn't take it, someone else must have.
- Anita says 'Sunil is truth-teller' - FALSE, so Anita is liar.
- Amit says 'I did not take it' - TRUE, so Amit is truth-teller.
- This gives Sunil=L, Amit=T, Anita=L with no thief identified - INCONSISTENT.
Therefore, the only consistent solution is Amit took the crystal.
- Amit took the crystal (from statement 1).
- Exactly one person took the item (from statement 4).
- Amit says 'I did not take it' - FALSE, so Amit is liar (consistent).
- Anita says 'Sunil is truth-teller' - TRUE, so Anita is truth-teller.
This gives: Sunil=T, Amit=L, Anita=T with Amit as thief.
Step 2: If Sunil is liar, then:
- Amit did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Amit didn't take it, someone else must have.
- Anita says 'Sunil is truth-teller' - FALSE, so Anita is liar.
- Amit says 'I did not take it' - TRUE, so Amit is truth-teller.
- This gives Sunil=L, Amit=T, Anita=L with no thief identified - INCONSISTENT.
Therefore, the only consistent solution is Amit took the crystal.