This may seem a very strange poll but I honestly want to know what others think. I just spent 1 hour writing out a full, rigourous solution to a problem. I formulated the main idea in about 5 minutes and I knew that my proof (once written out) would be correct. After spending about 12 times longer to write it out than "proving it in my mind" I wonder whether it was worth it (the question is not part of an assignment). On the one hand, I picked up details that was not in my mind at first, and my fully written solution is forever saved and I can look it up if I ever want to try the problem again. I also exercised my mathematical rigour and proof-writing in general. Besides, by writing it out I could have realized that the solution in my mind was wrong. On the other hand, I spent 12 times longer than solving it in my mind and I could have done many other questions in that time. So my poll question is: What is the greatest writing-time-to-thinking-time ratio that you would accept to write out the full solution to a problem? When I say thinking time, I mean solving the question in your mind (or scribbling the key ideas) to the point where you know you are correct (up to minor details that you know can be filled if you choose to write out the full solution). For example, if your ratio is 1:6, it means that if you can solve a problem in your mind in, say, 5 minutes, but it will take you 30 minutes to write it out fully (and the question is not an assignment question), you would just forego writing out the solution (or just scribble out the key ideas) and move on. Sorry I could not phrase the question more informally.