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Let's take your average Joe, and put him in a city of your choice. He is average in intelligence, investigative skills and so forth. He has some defensive capabilities but doesn't have much skills in martial arts. Every time he dies (by any means necessary), he resets to a random point 3-5 months before he died. He has to catch Patrick Bateman, Hannibal Lecter, Dexter, Norman Bates, and John Kramer. He has the opportunities to work with the authorities/relevant people there, and co-operate to some extent with whatever the best detectives have to offer, but he has to make the deductions by himself and catch the serial killers.
I'm excluding supernatural serial killers for obvious reasons...but he has to catch them within a year. However, he can reset as many times as he wants.
Note- for the people asking for clarification, the "within a year" condition applies even after he dies. For instance, if he starts in January of 2016, and he dies in February of the same year, he resets to December 2015 or before that and he has a period of one year from that reset point to catch the killer. He also has to gather evidence again since he won't have access to it, but he will be able to remember information from previous reset points.
There's a difference between "can store" and "can memorize" though. If you have a bag of liquid with all the same compounds as a brain, no matter how long you make it sit around there's no guarantee it will eventually become a brain, because infinite expression isn't the same as expressing all combinations.
I don't think the human mind as it is can memorize all of Wikipedia, it's just not good at storing information that way. Since the brain can't do it, it's the same as waiting for the bag of juice to turn into a brain.
given infinite loops the answer is always yes
Awctually, not really. Infinity doesn't guarantee the expression of all possibilities, even if they have a probability. It's easy to imagine sequences that are infinite but do not contain certain numbers; the series of all odd numbers contains no evens, for example.
In cases of infinite repetition, the person might go mad or develop a srug addiction and then spend all eternity catatonic. Especially given that the exact same things will happen again and again.
It's also never specified if human memory is expanded in this... I don't think a human could memorize the entirety of Wikipedia even given infinite time it they had to really use a physical human brain.
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I hope she's very tough then...