As long as we are trading anecdotes, let me share a story that happened to me.
A couple of years ago I was trying to solve a question for a collaborative take-home exam in a set-theory course. I spent an hour or so thinking about it and jotting in a notebook. I then tried to jog my brain by taking an hour-long walk while musing on the problem. At the end of this process I had made one or two relevant observations but was nowhere near solving it; my estimate at the time was that I had it about one-third solved.
The next day I met up with a classmate, we exchanged some easy observations, and solved it straight away. It took only a couple of minutes, and neither of us had to think particularly hard.
Of course the observations we had made individually helped, but we made up many of the ideas on the spot. At the time I was very impressed by how much more efficient we were when working together.
As long as we are trading anecdotes, let me share a story that happened to me.
A couple of years ago I was trying to solve a question for a collaborative take-home exam in a set-theory course. I spent an hour or so thinking about it and jotting in a notebook. I then tried to jog my brain by taking an hour-long walk while musing on the problem. At the end of this process I had made one or two relevant observations but was nowhere near solving it; my estimate at the time was that I had it about one-third solved.
The next day I met up with a classmate, we exchanged some easy observations, and solved it straight away. It took only a couple of minutes, and neither of us had to think particularly hard.
Of course the observations we had made individually helped, but we made up many of the ideas on the spot. At the time I was very impressed by how much more efficient we were when working together.