Problem #49 EASY
The Tea Estate Mystery
Scenario Logic Deduction Game Theory
Problem Statement
High up in the Nilgiri hills, Meera manages a sprawling tea estate that has been in her family for four generations. Every morning she walks the same path through rows of tea bushes, greeting the workers by name.
One morning, her estate manager Govind comes to her looking troubled. 'Someone has been stealing processed tea from the drying shed,' he says. 'We have narrowed it down to three workers who had access last night — Ashok, Bala, and Chandra.'
Meera calls all three men in and asks each one a single question: 'Did you steal the tea?'
Ashok says: 'I did not steal it. Bala is innocent.'
Bala says: 'I did not steal it. Chandra is guilty.'
Chandra says: 'I did not steal it. Ashok is lying.'
Meera already knows from previous experience that exactly one of the three men is the thief, and the thief always lies about everything. The innocent workers always tell the truth about everything.
Based on the three statements, who stole the tea?
Answer & Quick Explanation
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Chandra stole the tea. Assuming Chandra is the thief: his two statements are both lies (consistent for the thief). Ashok's two statements are both true and Bala's two statements are both true — consistent for innocent truth-tellers. No other assumption works.
Detailed Editorial Solution
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Use proof by assumption — assume person X is the thief and verify that all their statements are false (since the thief always lies) and all other statements are true (since innocents always tell the truth).
Step 1: Assume Ashok is the thief. His statements should both be lies: 'I did not steal' (lie — good, Ashok did steal) and 'Bala is innocent' (lie — meaning Bala is guilty). But we assumed only one thief. Contradiction — two thieves cannot exist. Ashok is not the thief.
Step 2: Assume Bala is the thief. His statements should both be lies: 'I did not steal' (lie — good) and 'Chandra is guilty' (lie — meaning Chandra is innocent). Now check the innocents.
Step 3: Ashok is innocent (truth-teller): 'I did not steal' (true — Ashok is innocent) and 'Bala is innocent' (false — Bala IS the thief). But Ashok should only say true things. Contradiction? Wait — Ashok says Bala is innocent, but Bala is guilty. That means Ashok's statement is false, making Ashok a liar — but Ashok is supposed to be innocent. Contradiction.
Step 4: Assume Chandra is the thief. His statements are both lies: 'I did not steal' (lie — good) and 'Ashok is lying' (lie — meaning Ashok is telling the truth).
Step 5: Check Ashok (innocent): 'I did not steal' (true) and 'Bala is innocent' (true — Bala is innocent if Chandra is the thief). Both true. Consistent.
Step 6: Check Bala (innocent): 'I did not steal' (true) and 'Chandra is guilty' (true — Chandra IS the thief). Both true. Fully consistent. Chandra is the thief.
Key Insight:
The method is systematic elimination: assume each person is the thief, derive what all statements must be (truths for innocents, lies for the thief), and check for contradictions. Only one assumption survives without contradiction — that is your answer.