Final answer:
By analyzing the four confessions and knowing that exactly one statement is false, it becomes clear that the guilty person is Person s, as individual p and s's matching accusations are both lies, q's accusation is the false statement, leaving only r's confession to be true.
Step-by-step explanation:
The question involves a logic puzzle where we need to determine which one out of four persons (p, q, r, s) committed a crime based on their confessions and knowing that exactly one of the statements is false.
Let's examine the statements:
- Person p says: q did it.
- Person q says: s did it.
- Person r says: I did not do it.
- Person s says: q did it (the same as Person p's statement).
If Person p's statement is true, then Person s's statement also has to be true. However, this would result in two people telling the truth, contradicting the information that only one statement is false. Therefore, both p and s must be lying if they accuse the same person, q. Now we only have two statements left; we know that one is true (since only one is false) and one must be false. If we consider Person q's statement (s did it) is true, then Person r's statement (I did not do it) has to be false, which would imply r did it. However, this contradicts q's statement. Thus, Person q's statement is the false one, and by process of elimination, Person r's statement I did not do it is the true one, meaning r is innocent. Therefore, the guilty party must be Person s.