Four statements, one snatching, one camera that was not working
On a Saturday evening a gold chain is snatched near the Upper Bazaar bus stand in Ranchi. The complainant says the snatcher fled on a motorcycle. Four employees of a nearby shop, the only persons close to the spot, are questioned the same night. Each gives exactly one statement: Ravi: 'Sunil did it.' Sunil: 'Tariq did it.' Tariq: 'Sunil is lying.' Umesh: 'I did not do it.' The control room tells the investigating officer that the offence was committed by exactly one of these four men, and the CCTV camera at the stand was not working that evening. The officer also has before him a note from an earlier case in the same thana in which four statements of the same pattern were recorded and exactly one of them later proved true. The officer must decide tonight whether to name a suspect in the case diary or to keep all four as suspects and call for more evidence before the remand file goes up.
1. Assuming exactly one of the four statements is true, identify the offender and set out the reasoning step by step.
Read the worked answer
Step 1 - spot the contradictory pair. Sunil says Tariq did it; Tariq says Sunil is lying, i.e. Tariq did not do it. These two statements cannot both be true and cannot both be false: exactly one of the pair must be true.
Step 2 - use the 'only one true' condition. Since one of Sunil's or Tariq's statements is the single true statement, Ravi's statement and Umesh's statement must both be false.
Step 3 - act on Umesh. Umesh said 'I did not do it.' That is false, therefore Umesh did it.
Step 4 - verify against every statement. If Umesh is the offender:
- Ravi: 'Sunil did it' - false. Correct.
- Sunil: 'Tariq did it' - false. Correct.
- Tariq: 'Sunil is lying' - true, because Sunil's statement is indeed false. Correct.
- Umesh: 'I did not do it' - false. Correct.
Total true statements = exactly one. The assumption is satisfied, so the answer is consistent and unique.
Step 5 - the exam trap. Many candidates stop at 'one of Sunil/Tariq is true' and conclude the case is undecidable. It is decidable, but only because the 'exactly one true' condition forces the other two statements to be false. Without that condition the puzzle has no unique solution.
2. Suppose instead the officer learns that exactly two of the statements are true. Can he now name a single offender? Show your working.
Read the worked answer
Test each candidate as offender and count the true statements:
| Offender | Ravi | Sunil | Tariq | Umesh | True count |
|---|---|---|---|---|---|
| Ravi | F | F | T | T | 2 |
| Sunil | T | F | T | T | 3 |
| Tariq | F | T | F | T | 2 |
| Umesh | F | F | T | F | 1 |
Conclusion. A two-true-statement condition is satisfied both when Ravi is the offender and when Tariq is the offender. The evidence is insufficient; the officer cannot name either man on the statements alone.
Why this matters operationally. Naming a suspect in the case diary on a two-solution fact pattern is a real risk: the remand file goes up on a named person who has a 50 per cent chance of being innocent, and the actual offender learns from the arrest that he is being looked for. The correct entry is to record both Ravi and Tariq as suspects, record the reasoning above, and state expressly that the statements do not discriminate between them.
What would discriminate. Something external to the statements: who was absent from the shop counter at the relevant minutes, who owns or had access to a motorcycle, the complainant's description of clothing and build, and any usable footage from the shop's own camera or a neighbouring one. Under Section 161 CrPC the four statements are not evidence in the strict sense anyway; they are investigative leads, and the same is true of the corrected ones.
3. What should the officer put in the case diary tonight, and which further steps should he order?
Read the worked answer
Case diary entry. Record verbatim the four statements, the control room information, the non-working camera, and the full truth-table analysis, including the alternative outcome under the two-true hypothesis. An entry that shows the reasoning protects the investigation if the logic is later challenged and shows the magistrate that arrest was not arbitrary.
Do not (a) arrest Umesh on the statements alone without at least one independent link, (b) confront all four together in one room, which lets them align their versions, or (c) disclose to any of them what the others said.
Steps worth ordering the same night.
- Separately re-examine each man on time, place, clothing and motorcycle access, and record the answers in their own words.
- Seize and view footage from the shop camera facing the bus stand, plus any private camera on the route of escape, and preserve it under a seizure memo before it overwrites.
- Trace the motorcycle through the registered owner and check for a stolen or untraceable vehicle.
- Take the complainant's description of the chain and the rider, and hold an identification parade later in accordance with law rather than showing photographs of all four at once.
- Verify whether any of the four has a prior snatching entry. Rule to state in the note: a confession-style statement is a lead, corroboration is proof; the file must show which is which.