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christopherj comments on The Absent-Minded Driver - Less Wrong
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If you're allowed to use external memory, why not just write down how many you painted of each color? Note that memory is different from a random number generator; for example, a random number generator can be used (imperfectly) to coordinate with a group of people with no communication, whereas memory would require communication but could give perfect results.
Have you read this comment of mine from another branch of this conversation?