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Memorizing 100 random symbols for the most important logins is reasonable, but the average person probably has in the order of 50 logins or so. I just counted and was surprised that my password manager contains over 200 passwords. There is no way that I could memorize that many secure passwords or even passphrases.

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FWIW, and I'm not suggesting you actually do this, but you probably could learn to remember that many symbols. People can memorize thousands of digits of pi. People can solve ~60 rubik's cubes in an hour blindfolded (where they must first memorize them). I think, surprisingly, it's actually within the realm of human ability to memorize 200 20 character passwords.

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