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dhasenan comments on What false beliefs have you held and why were you wrong? - Less Wrong Discussion
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One of the smartest people in my high school spent a class arguing that a there were 4^20 possibilities for a sequence of 4 amino acids, when in fact it was 20^4. Not quite as elementary as yours, but our brains all play tricks on us.
Wikipedia says there are 500 known amino acids. I take it you were talking about a domain involving fewer potential amino acids?
The 20 amino acids involved in protein creation.
Presumably the slightly greater than twenty that form the universal basis of biological protein polymers. In other words, the amino acids explicitly coded for by DNA.