Let's solve this logic puzzle about three boxes. We have a red box, a blue box, and a yellow box. The red box claims it has the ball. The blue box says it doesn't have the ball. And the yellow box states that the red box doesn't have the ball. We're told that only one of these statements is true. Our task is to determine which box contains the ball.
Let's analyze the statements made by each box. The red box claims it has the ball. The blue box says it doesn't have the ball. And the yellow box states that the red box doesn't have the ball. An important observation is that the statements from the red box and the yellow box directly contradict each other. If the red box has the ball, then the yellow box's statement is false. And if the yellow box is telling the truth, then the red box's statement must be false. Since they contradict each other, at most one of these two statements can be true.
Now, let's deduce which box has the ball. We know that exactly one statement is true. Since the statements from the red and yellow boxes contradict each other, one of them must be the true statement. This means the blue box's statement must be false. If the blue box's statement is false, then the blue box must have the ball. Let's verify this solution: If the blue box has the ball, then the red box's statement 'I have the ball' is false. The blue box's statement 'I don't have the ball' is also false. And the yellow box's statement 'The red box doesn't have the ball' is true. This gives us exactly one true statement, which matches our condition. Therefore, the blue box has the ball.
To summarize our solution: We identified that the statements from the red and yellow boxes contradict each other, so one must be true and one must be false. Since only one statement can be true overall, the blue box's statement must be false. If the blue box's statement is false, then the blue box must have the ball. This scenario gives us exactly one true statement - the yellow box's statement - which satisfies our condition. Therefore, we can confidently conclude that the blue box has the ball.
Let's review the key takeaways from this logic puzzle. First, logic puzzles can often be solved by carefully analyzing contradictions and constraints. When statements contradict each other, they can't both be true simultaneously, which helps narrow down possibilities. Working backward from the given constraints is a powerful problem-solving strategy. Always verify your answer against all the conditions to ensure it's correct. In this particular puzzle, we determined that the blue box has the ball, with the yellow box being the only one telling the truth. This type of logical reasoning is useful not just for puzzles, but in many real-world situations that require critical thinking.