Under a certain legal system, prisoners are allowed to make one statement. If their statement turns out to be true then they are hanged. If the statement turns out to be false then they are shot. One prisoner made a statement and the judge had no option but to set him free. Which one of the following could be the prisoner's statement?
A. "I will be shot" B. "I will be set free" C. "I committed the crime" D. "You committed the crime"
GATE 2019 · General Aptitude · Verbal Reasoning · medium
Answer: The prisoner says 'I will be shot.' This creates an unresolvable logical paradox under both truth assumptions, leaving the judge with no option but to set the prisoner free. Answer: A.
Test option A: 'I will be shot': Assume the statement is TRUE: prisoner spoke truly, so must be hanged (not shot). But then the statement 'I will be shot' is FALSE — contradiction. Now assume FALSE: prisoner lied, so must be shot. But then the statement 'I will be shot' is TRUE — contradiction again. Both assumptions lead to contradiction. The judge cannot act — must set the prisoner free.
Test option B: 'I will be set free': If TRUE: prisoner is hanged (not set free) — the statement becomes false. If FALSE: prisoner is shot (not set free) — the statement remains false. In the false case there is no contradiction; the prisoner is simply shot. This is not a paradox. Option B does not force freedom.
Test options C and D: factual statements: 'I committed the crime' and 'You committed the crime' are verifiable factual claims. If true, prisoner is hanged. If false, prisoner is shot. Neither creates a self-referential loop. The judge can always apply one of the two punishments.