Reverse engineering magic tricks is very, very hard. Sometimes I'll watch a good sleight or illusion over and over again on video before I can even guess how it is done.
Back in 1984 Feynman attended a lecture at Caltech given by James Amazing Randi, a well known magician and debunker of psychics. At this lecture, Randi performed a very good mental trick involving a newspaper and a prediction contained in an envelope pasted to the blackboard. The next evening, Randi and Feynman were at my house for dinner. It was a delightful and fun evening with lots of jokes and laughter all around. At about 1:30 a.m., Feynman and Randi still going strong, Feynman decided to figure out how Randi did his mental trick. Oh, no. You can't solve that trick. You don't have enough information! Randi exclaimed. What do you mean? Physicists never have enough information, Feynman responded. Feynman began to stare off into space with Randi muttering on how he would not be able to solve it. Step by step, Feynman went through the process out loud and told Randi how the trick must have been done. Randi literally fell backwards over his chair and exclaimed, You didn't fall off no apple cart! You didn't get that Swedish Prize for nothing! Feynman roared with laughter. Later, on another visit to Caltech, Randi once again joined us for lunch. He did another trick for Feynman, this time a card trick. I DELIBERATELY misled you this time! Randi stated. Feynman paid him no attention. In less than three minutes, Feynman solved the trick. I'm never going to show you another trick again! declared a frustrated Randi.
I found this anecdote here. (Thanks to commenter on earlier thread for the pointer.) Below is another involving Roger Penrose.
Not long ago I gave a lecture at Oxford University. While I was there I had the good fortune to have a long lunch with physicist/mathematician Roger Penrose, who is responsible for much of our understanding of black holes. The topic of Feynman came up and Penrose related the following story: A while back he was visiting Caltech with Steven Hawking. Hawking asked Penrose if there was anyone at Caltech that he wanted to meet. The choice obviously came down to either Feynman or Gell-Mann. Penrose decided they should try to get a hold of Feynman. Hawking called up the office, but Feynman wasn't in. He was on vacation. It turns out, however, he was vacationing at his home. Hawking called Feynman at home and Feynman reluctantly agreed to come over the next day. The subject of quantum gravity came up and Penrose and Feynman got into a heated argument. Penrose said, Feynman was so quick, he was usually about five steps ahead of me at any given point. Sometimes he didn't listen to what I was saying. The whole thing was mentally exhausting. I was completely drained at the end of the session. I have never encountered anyone so quick before. What Penrose and many other physicists didn't realize was the reason that accounted for Feynman's quickness on many matters in physics. Feynman thought about some of these areas in great depth and for long periods of time. A topic like quantum gravity would be one that Feynman had spent countless hours thinking about. It wasn't all off the cuff.