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The police arrested four criminals - P, Q, R and S. The criminals knew each other. They made the following statements: P says “Q committed the crime.” Q says “S committed the crime.” R says “I did not do it.” S says “What Q said about me is false.” Assume only one of the arrested four committed the crime and only one of the statements made above is true. Who committed the crime?

The police arrested four criminals - P, Q, R and S. The criminals knew each other. They made the following statements: P says “Q committed the crime.” Q says “S committed the crime.” R says “I did not do it.” S says “What Q said about me is false.” Assume only one of the arrested four committed the crime and only one of the statements made above is true. Who committed the crime? Correct Answer R

Let S1: P says “Q committed the crime.”

S2: Q says “S committed the crime.”

S3: R says “I did not do it.”

S4: S says “What Q said about me is false.”

1. Assume that P committed the crime:

S1 is false, S2 is false, S3 is true, S4 is true

Since S3 and S4 are true, R and S says true but only one of the statements among S1, S2, S3 and S4 is true. Therefore, assuming that P committed the crime is false.

2. Assume that R committed the crime:

S1 is false, S2 is false, S3 is false, S4 is true

Since S4 is true, S says true and only one of the statements among S1, S2, S3 and S4 is true. Therefore, assuming that R committed the crime is true.

3. Assume that S committed the crime:

S1 is false, S2 is true, S3 is true, S4 is false

Since S2 and S3 are true, Q and R both says true but only one of the statements among S1, S2, S3 and S4 is true. Therefore, assuming that S committed the crime is false.

4. Assume that Q committed the crime:

S1 is true, S2 is false, S3 is true, S4 is true

Since S1, S3 and S4 are true, P, R and S says true but only one of the statements among S1, S2, S3 and S4 is true. Therefore, assuming that Q committed the crime is false.

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