I was at the table with two people who had trouble solving the problem, which I blazed through in about 30 seconds. The teacher came by and asked who had a solution, and when I was the only one at my table who did, she gave me the task of teaching the solution to the rest of the table. She also said she would ask one of them to present the answer to the rest of the class.
That is when the class got interesting. There was one exceptionally vocal student who kept interrupting me as I tried to explain my answer, literally before I completed more the two sentences. Getting her passive enough for the rest of the table to hear me was a fantastic teaching exercise. The weird thing was that she was so excited and positive, not intentionally obstructive.
I ended up getting the answer and justification across to everyone except her, and I've been thinking about what I could have done differently ever since. She had the impression that she understood, but when she volunteered to present (of course she did) it was clear she didn't understand.
One of the students was concerned about how quickly I got the answer and why I knew how to solve it, but she didn't even though she had a math minor. I tried to console her with the line that I've been working in a math intensive environment for decades, but I'm not convinced that was the best answer.
Now I have two homework assignments. One is to write up my math learning history; the other to design several lesson plans around the problem above based on different levels of sophistication in talking about the problem.
I'm going to like being a student again.