Andy Yao was my first research mentor, when I was a visiting student in Princeton. After he had given me an open problem and we discussed it for a couple of weeks, he formulated an intermediate conjecture. If we could prove it, it would be a step forward. If we found a counter-example, it would give us new insight on the hidden difficulties.
Then he said: "Let's take a bet. Let's both try to resolve this question before we meet again next week, and let the stake of the bet be a dinner".
I couldn't pass up such a challenge, of course. I worked on the question intensively until I had solved it, a couple of days later. It made me so happy! I could barely contain my excitement. Later that day I saw Andy Yao at a seminar that we were both attending, and, unable to wait until the end of the talk, I leaned towards him and whispered with a big smile: "I solved it!" - and then, a little anxiously: "How about you, did you solve it?" No, he had not solved it. He said he was looking forward to hearing my solution during our next meeting.
And so, a few days later, we went (along with Kai Li) to a very good Chinese restaurant on Route 1 for dinner. Andy ordered lots of food, and, in particular, some fresh lobster. But I had never had that before and didn't know how to eat it properly, so I politely declined the lobster, contenting myself with the other dishes. In my memory, the dinner was delicious.
Now I see that that bet was an obvious ploy to get the student interested. I fell for it completely! What a great idea.