CombinatoricsDifficulty 4.5AIMEFind the answerSlovenia
During the course of a crime investigation 4 suspects have been arrested. Each of them gave a statement.
Žan: "Of all the suspects only I am innocent." Alen: "Of all the suspects only I am guilty." Zala: "We are all innocent." Beno: "At least 2 of the suspects are guilty."
Further investigation has shown that at least one of the suspects was guilty and the innocent were telling the truth while the guilty were lying. How many of the suspects were guilty?
Pick one
Solution
Alen cannot be innocent since that would imply that he is telling the truth and would be, according to his own statement, guilty. Hence, Alen is guilty. From here we conclude that Zala was lying and must, therefore, also be guilty. Now, we see that Beno was telling the truth and is innocent. Finally, Žan must have been lying, so he must be guilty as well. Precisely three of the suspects were guilty, namely Žan, Alen and Zala.
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