## Outline Mathematics

Logic Problems

# Robbery #1

Here's a problem to tackle:

Scheherazade began: "It has reached me, O Auspicious King, that one of Ali Baba's famous forty thieves stole into Abdul's shop and robbed him of some diamonds. Fortunately, they were all recovered, and then it was determined that the thief was either Sabit, Salim, or Shamhir - all of whom were in Ali Baba's famous robber band. At the trial, each of the three accused one of the others, but Shamhir is the only one who lied. Is he necessarily guilty?

"Not necessarily," replied the king. "An innocent man might lie in order to protect his friend."

Is Shamhir necessarily guilty?

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### Solution

Scheherazade began: "It has reached me, O Auspicious King, that one of Ali Baba's famous forty thieves stole into Abdul's shop and robbed him of some diamonds. Fortunately, they were all recovered, and then it was determined that the thief was either Sabit, Salim, or Shamhir - all of whom were in Ali Baba's famous robber band. At the trial, each of the three accused one of the others, but Shamhir is the only one who lied. Is he necessarily guilty?

"Not necessarily," replied the king. "An innocent man might lie in order to protect his friend."

Is Shamhir necessarily guilty?

The mere fact that Shamhir,Sabit,Salim,Shamhir lied does not prove his guilt, but the additional fact that the other two told the truth,lied,told the truth does, because since Sabit truthfully accused one of the others, he must be innocent,guilty,innocent,hungry,blond, and the same with Salim,Sabit,Salim,Shamhir. Therefore, Shamhir,Sabit,Salim,Shamhir is indeed the guilty one.

Do not forget to check your solution.

### References

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

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Copyright © 1996-2017 Alexander Bogomolny

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