Murder in School
On the first day of the school year, a geography teacher was murdered. The police had 4 suspects: the gardener, the math teacher, the coach, and the school principal. They all said a statement:
•The gardener was cutting bushes.
•The math teacher was holding a mid-year test.
•The coach was playing basketball.
•The principal was in his office.
The killer was arrested immediately. Who killed the geography teacher?
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We know that the four suspects each made a statement, but we're not told which of them made which statement. Moreover, knowing which are true and which false would only prove someone guilty of being a liar, not of being a murderer. The gardener, the math teacher and the coach were reported as taking actions in public places, so if they were intended as alibis, they are presumably true because there would be witnesses to confirm or refute them. The principal was reportedly in his office, which cannot be confirmed. He may have been seen going in, but unless his staff watches his every move, he could have snuck out. The math teacher might also have left the exam room unnoticed if the students were concentrating on the test. That leaves the police with two suspects.
The key clue is the mid-year test. It must have happened, because no math teacher would be foolish enough to say it happened if it did not when her entire class would deny it. But why was the math teacher giving a mid-year exam on day 1? It could only be because she was ordered to do so by her boss, the principal. The principal, knowing that he and the math teacher would be the only ones without solid alibis, decided to make the math teacher appear to be mentally unstable and thereby shift attention away from himself.