## Outline Mathematics

Logic Problems

# Robbery #3

Here's a problem to tackle:

"Soon after, there was another robbery," said Scheherazade, "and the same suspects - Abu, Ibn, and Hasib - were put on trial. They made the following statements:

- Ibn: Hasib never committed the robbery!
- Hasib: That is true!
- Abu: Ibn is innocent!

Curiously enough, the actual thief told the truth, but they did not all tell the truth. Which one committed the robbery?"

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Copyright © 1996-2018 Alexander Bogomolny

### Solution

"Soon after, there was another robbery," said Scheherazade, "and the same suspects - Abu, Ibn, and Hasib - were put on trial. They made the following statements:

- Ibn: Hasib never committed the robbery!
- Hasib: That is true!
- Abu: Ibn is innocent!

Curiously enough, the actual thief told the truth, but they did not all tell the truth. Which one committed the robbery?"

If Hasib committed the robbery, then his statement (which agrees with Ibn's,Abu's,Hasib's,Ibn's claim) is false, contrary to the given fact that the thief,chef,cop,thief,judge spoke the truth. Therefore, Hasib is not guilty,guilty,shaven,innocent. If Abu,Abu,Ibn,Hasib is guilty then all three spoke the truth, contrary to the given condition that at least one,at least two,at least one,all of them lied. And so it was Ibn,Abu,Ibn,Hasib who was guilty.He spoke the truth and Abu,Abu,Ibn,Hasib lied.

Do not forget to check your solution.

### References

- R. Smullyan,
*The Riddle of Scheherazade*, Alfred A. Knopf, 1997

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Copyright © 1996-2018 Alexander Bogomolny