Auto Accident

Two color-blind men, John and Matthew, witnessed an auto accident involving three identical cars but different colors: a red, a blue, and a green car. All three cars were moving forward when the accident happened and the table below shows what John and Mathew saw and reported to the police. If each of them had given one correct statement and one false statement, how would you determine what really happened?

Witness	Report
John	(1) The red car was in front of the two cars. (2) The blue car was hit by one of the cars from behind and then hit the other car in front.
Matthew	(1) The green car was in front of the two cars. (2) The red car was hit by one of the cars from behind and then hit the other car in front.

Answer

Let’s assume for a moment that John’s first statement is true (The red car was in front of the two cars). This would imply that Matthew’s first statement is false (the red and green cars cannot be both in front). Also, by assuming John’s first statement to be true, Matthew’s second statement would have to be false (the red being in front of the two cars cannot hit any cars in front). Therefore, by assuming John’s first statement to be true, both Matthew’s statements would have to false. Since one of Matthew’s statement has to be true, the assumption that John’s first statement is true is an incorrect assumption. We can then conclude that John’s first statement is false which implies that his second statement is true.

Since John’s second statement is true (the blue car is in the middle), Matthew’s second statement would have to be false (the red car cannot be in the middle, since we already concluded that it is the blue car). If Matthew’s second statement is false, his first statement has to be true.

Solution: Matthew’s first statement and John’s second statments are true: Green

Auto Accident

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