"Tonight", said the Sultan to Scheherazade, "let's see how clever you are. I have a problem for you." "Well," said Scheherazade, "that certainly makes a change." "Rashid, my museum curator," said the Sultan, "told me this morning that one of Omar Khayyam's rare and valuable manuscripts has been stolen." "Omar Khayyam?" said Scheherazade, "but he's Persian. How come one of his manuscripts is in a Baghdad museum?" "Never mind that" said the Sultan testily, "anyway, it isn't, is it? It's gone. And Rashid has three suspects: Abdul, Bahir and Dabir. They've been questioned and Rashid tells me that each has made one true and two false statements. They are as follows:
Abdul:
1. I didn't know that the museum had anything of Omar Khayyam's.
2. Dabir is innocent.
3. Bahir is the thief.
Bahir:
1. I didn't steal it.
2. Abdul is innocent.
3. Abdul's first statement is true.
Dabir:
1. Omar's writings are not worth stealing.
2. Abdul stole it; or else it was Bahir.
3. I would never do such a dishonest thing.
Rashid says that Hanif, the Chief of Police, is useless, and that his (Rashid's) headache prevents him from solving the problem. Now," continued the Sultan, "what have you to say?" And Scheherazade, who was probably a distant ancestor of Alice, soon arrived at the solution and named the culprit. Which was?
(Acknowledgement: Raymond Smullyan

Here's a hint. Begin by assuming that Bahir is guilty. On this assumption, test each of his statements against the conditions, i.e. that he has made one true statement and two false statements.

Statements:
Abdul:
A1. I didn't know that the museum had anything of Omar Khayyam's.
A2. Dabir is innocent.
A3. Bahir is the thief.
Bahir:
B1. I didn't steal it.
B2. Abdul is innocent.
B3. Abdul's first statement is true.
Dabir:
D1. Omar's writings are not worth stealing.
D2. Abdul stole it; or else it was Bahir.
D3. I would never do such a dishonest thing.
Each has made one true and two false statements.

Assume that Bahir is guilty. If so, A2 and A3 are true. But they can't both be true, so Bahir isn't guilty.
Assume that Dabir is guilty. If so, B1 and B2 are true. They can't both be true either, so Dabir isn't guilty. It must have been Abdul.
A1, A3 - false, A2 - true.
B1 - true, B2, B3 false.
D1, D3 - false, D2 - true.