Car Collection Logic Puzzle Explained

This problem is a classic example of a logical reasoning puzzle where we need to deduce the correct number of cars owned by S based on conflicting statements from three individuals, P, Q, and R, with the crucial condition that only one of them is telling the truth.

Understanding the Statements

Let's first break down each person's statement about S's car collection:

• P's statement: "S has at least 3 cars." This can be mathematically represented as $\text{S} \geq 3$.
• Q's statement: "S has less than 3 cars." This can be mathematically represented as $\text{S} < 3$.
• R's statement: "To his knowledge, S has at least one car." This can be mathematically represented as $\text{S} \geq 1$.

The core condition given is that only one of P, Q, and R is right (i.e., their statement is true).

Analyzing Possible Scenarios for S's Cars

To find the correct number of cars S owns, we will test different possible numbers of cars and see which scenario satisfies the condition that exactly one statement is true. We'll evaluate each statement (True or False) for various values of S.

Step-by-Step Evaluation

Let's examine each possible number of cars for S in detail:

• Case 1: S owns 0 cars
  • P states $\text{S} \geq 3$: This is False, as $0$ is not greater than or equal to $3$.
  • Q states $\text{S} < 3$: This is True, as $0$ is less than $3$.
  • R states $\text{S} \geq 1$: This is False, as $0$ is not greater than or equal to $1$.
  • In this case, only Q's statement is true. This satisfies the condition that "only one of P, Q and R is right."
• Case 2: S owns 1 car
  • P states $\text{S} \geq 3$: This is False, as $1$ is not greater than or equal to $3$.
  • Q states $\text{S} < 3$: This is True, as $1$ is less than $3$.
  • R states $\text{S} \geq 1$: This is True, as $1$ is greater than or equal to $1$.
  • In this case, both Q and R's statements are true. This violates the condition that "only one of P, Q and R is right."
• Case 3: S owns 2 cars
  • P states $\text{S} \geq 3$: This is False, as $2$ is not greater than or equal to $3$.
  • Q states $\text{S} < 3$: This is True, as $2$ is less than $3$.
  • R states $\text{S} \geq 1$: This is True, as $2$ is greater than or equal to $1$.
  • Similar to the previous case, both Q and R's statements are true. This violates the condition.
• Case 4: S owns 3 cars
  • P states $\text{S} \geq 3$: This is True, as $3$ is greater than or equal to $3$.
  • Q states $\text{S} < 3$: This is False, as $3$ is not less than $3$.
  • R states $\text{S} \geq 1$: This is True, as $3$ is greater than or equal to $1$.
  • Here, both P and R's statements are true. This again violates the condition.
• Case 5: S owns more than 3 cars (e.g., S = 4)
  • P states $\text{S} \geq 3$: This is True, as $4$ is greater than or equal to $3$.
  • Q states $\text{S} < 3$: This is False, as $4$ is not less than $3$.
  • R states $\text{S} \geq 1$: This is True, as $4$ is greater than or equal to $1$.
  • Again, both P and R's statements are true. This violates the condition.

Conclusion on S's Car Collection

Based on the detailed analysis of all possible scenarios, the only number of cars for S that satisfies the condition that "only one of P, Q, and R is right" is 0. In this specific situation, Q's statement ("S has less than 3 cars") is true, while P's and R's statements are false.

Therefore, the number of cars owned by S is 0.