I had an intractable code issue with my stats this week and I couldn't solve it for hours. At long last exactly two things solved it: 1) getting a better night's sleep 2) giving up and working on something I thought was totally separate which turned out to contain the solution
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One of the best methods to solve really complex problems is to do something else and let your subconscious tackle it -- it's amazing how it can just pull the solution from the most mundane things.