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?

Option 2 : 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