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AIME 1991 Problem 13

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A drawer contains a mixture of red socks and blue socks, at most 19911991 in all. It so happens that, when two socks are selected randomly without replacement, there is a probability of exactly 12\frac{1}{2} that both are red or both are blue. What is the largest possible number of red socks in the drawer that is consistent with this data?

Dataset text AIME 1983 to 2026. Quoted with source.

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990

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