polymathwannabe comments on Harry Potter and the Methods of Rationality discussion thread, March 2015, chapter 119 - Less Wrong Discussion
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So the Stone was created to be used no more than 400 times a day. This allows for the prediction that someone with a normal cycle should be able to use it every 1/400 of our normal days, or 216 seconds.
The limit might be the result of limited capacity rather than design.