My favorite (and only) Talmud joke:
The Priest meets his friend, the Rabbi, and says to him "I would like you to teach me the Talmud."
The Rabbi replied: "You are a Non-Jew and you have the brain of a Non-Jew. There is no chance that you will succeed in understanding the Talmud."
But the Priest continued in his attempt to persuade the Rabbi to teach him the Talmud.
Finally, the Rabbi agreed. The Rabbi said to the Priest: "I agree to teach you the Talmud on condition that you answer one question." The Priest agreed and asked the Rabbi "What is the Question?"
The Rabbi then said: "Two men fall down through the chimney. One comes out dirty and the other comes out clean. Who of those two goes to wash up?" Says the priest: "The one who is dirty goes to wash up but the one who is clean does not go to wash up."
The Rabbi then says: "I told you that you will not succeed in understanding the Talmud. The exact opposite happened. The clean one looks at the dirty one and thinks that he is also dirty, goes to wash up. The dirty one, on the other hand, looks at the clean one and thinks that he is also clean and, therefore, does not go to wash up."
"Ask me another!" says the Priest.
The Rabbi then says: "Two men fall down through the chimney. One comes out dirty and the other comes out clean. Who of these two goes to wash up?"
The Priest says: "The clean one looks at the dirty one and thinks he is also dirty and goes to wash up. The dirty one, on the other hand, looks at the clean one and thinks that he is also clean and, therefore, does not go to wash up."
The Rabbi then says: "Wrong again. I told you that you will not understand. The clean one looks into the mirror, sees that he is clean and, therefore, does not go to wash up. The dirty one looks into the mirror, sees that he is dirty and goes to wash up."
The Priest complains to the Rabbi "But you did not tell me that there is a mirror there." Says the Rabbi: "According to the Talmud, you have to think of all the possibilities."
"Alright," groaning, says the Priest to the Rabbi. "Ask me one more question."
For the last time, said the Rabbi, "Two men fall through the chimney. One came out dirty and the other came out clean. Who of these two went to wash up?"
"That is very simple!" replied the Priest. "If there is no mirror there the clean one will go to wash up. If there is a mirror there, the clean one will not go to wash up.!"
The Rabbi then says to the Priest: "I told that you will not succeed in understanding, you don't have a Jewish brain. Tell me, how is it possible for two men to fall through a chimney and for one to come out dirty and for the other to come out clean?"