I always keep a pad, a pen and a voice recorder on my night stand, right next to the alarm clock. Too many times I woke up in the middle of the night with the answer to a difficult problem or a great idea, only to have it totally evaporate by morning.
Re^2: Answers come to me when ...
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another vote for "while sleeping"!! i was surprised to see that "waking up" was an option, while i find that the process of waking often seems to dissipate the answer - ergo the notepad by the bed is particularly useful (although i often forget to be so foresighted!)