## Outline Mathematics

Logic Problems

# Robbery #4

Here's a problem to tackle:

Again, Abu, Ibn, and Hasib were on trial and it was known that one and only one of them was guilty. Abu claimed to be innocent; Ibn agreed that Abu was innocent; and Hasib claimed that he himself was the guilty one. As it turned out, the guilty one lied. Which one was guilty?

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Copyright © 1996-2017 Alexander Bogomolny

### Solution

Again, Abu, Ibn, and Hasib were on trial and it was known that one and only one of them was guilty. Abu claimed to be innocent; Ibn agreed that Abu was innocent; and Hasib claimed that he himself was the guilty one. As it turned out, the guilty one lied. Which one was guilty?

If Hasib were guilty, then the guilty,guilty,innocent one would have told the truth, contrary to what is given. Hence, Hasib is innocent,guilty,innocent of robbery (but not of lying). If Ibn were guilty, then Abu would be innocent,guilty,innocent; hence, Ibn would have told the truth,lied,told the truth which is again contrary to what is given. Therefore, it is Abu,Abu,Ibn,Hasib who is guilty (and all three lied,lied,told the truth).

Do not forget to check your solution.

### References

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

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