Three Jewels Problem (From `Brain Bogglers' by Raymond Smullyan)

Three ladies of the sultan's kingdom Amina, Fatin, and Safie each owned a precious jewel, one a diamond, one an emerald, and one a ruby, but we don't know who owned which. One day Abu, Badri, and Kisra each stole a jewel from one of the ladies, but it was not known who stole what from whom. The case proved extremely baffling, but fortunately Omar, the Persian sage, was visiting the country at the time and found the following facts, which were enough to solve the case.

• The one who stole the diamond is a bachelor and is the most dangerous of the three thieves.
• Amina is younger than the lady who owns the emerald.
• Abu's brother-in-law Kisra, who stole from the eldest of the three ladies, is less dangerous than the one who stole the emerald.
• The man who stole from Amina is an only child.
• Abu did not steal from Fatin.

Who stole what from whom?

Show that the sum of the interior angle of any n-gon is 180(n-2).

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