One Statement Must Be False: Testing a Chain-Snatching Charge
Three men, A, B and C, are questioned about a chain-snatching at 19:42 near a bus stand. Each makes one statement, recorded verbatim in the case diary: A: 'C snatched the chain.' B: 'A is lying.' C: 'B snatched the chain.' The investigating officer's working note records that exactly one of the three statements is false and the other two are true. On that basis he proposes to name B as the accused in the charge sheet. A fourth person, D, later tells a constable that he saw A running with a gold chain at about 19:45, some 400 m from the spot. The investigating officer now writes that the case is 'fully proved' against both A and B and that D's statement 'confirms' the earlier finding.
1. Test each possible culprit against the condition that exactly one statement is false, and state who can actually be named.
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Work through the three hypotheses systematically.
If A did it: A's statement ('C snatched') is false; A is therefore lying, so B's statement is true; C's statement ('B snatched') is false. That gives two false statements - the condition is violated.
If B did it: A's statement is false; A is lying, so B's statement is true; C's statement is true. Exactly one false - the condition holds.
If C did it: A's statement is true; A is not lying, so B's statement is false; C's statement is false. Two false statements - violated.
Conclusion: only B fits the single premise the officer has written down. The reasoning is not that B's guilt has been proved by evidence; it is that B is the only person consistent with the officer's own note. That distinction matters, because everything now rests on the note being correct. The charge sheet should say so, and the note should record who supplied the 'exactly one false' information and on what basis - if it came from an informer or from the officer's own impression, it is an assumption and must be labelled as one.
2. How should the investigating officer treat D's statement?
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Consistency is not corroboration. D's account places A, not B, with a gold chain shortly after the offence, 400 m away. It does not contradict B's guilt - two men can be involved in a snatching - and it does not confirm it either.
What the officer should do:
- Record D's statement properly and examine him; a statement to a constable is a lead, not evidence on which a charge sheet is built.
- Establish whether the chain D saw was the snatched chain (description, weight, identification by the complainant) and whether it was recovered from A.
- Test D's opportunity to observe: light at 19:45, distance, obstructions, duration of observation.
- Consider the three innocent explanations - A was an accomplice, A was carrying his own chain, or D is mistaken about the person.
Writing 'fully proved against both A and B' is not supported by anything on the record. The logical constraint identified B alone; adding A requires independent material, and D's unverified statement is not that material. 'Confirms the earlier finding' should be deleted from the note; it asserts a relationship that the reasoning does not support.
3. Suppose the officer's note is corrected to say that two of the three statements are false. What then follows?
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Re-run the three hypotheses against 'two false, one true'.
If A did it: A false, B true, C false - two false. Holds. If B did it: A false, B true, C true - one false. Fails. If C did it: A true, B false, C false - two false. Holds.
Result: A or C, and B is positively excluded. The identification has flipped completely.
This is the point the case should teach. The original conclusion that B was the snatcher depended entirely on a single premise - 'exactly one statement is false' - and nothing else. Change that one number and the accused changes from B to A or C. A premise that fragile cannot support a charge sheet; it must be either proved independently (for example, by showing the three statements were taken separately and one speaker had a demonstrable reason to lie) or discarded.
The practical lesson: in verbal reasoning questions of this type, first check whether the stated constraint is unique - if more than one arrangement satisfies it, the answer is 'cannot be determined', and in a police file that answer is written as further investigation required, not as a name.