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HMMT 2001 V6

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There are two red, two black, two white, and a positive but unknown number of blue socks in a drawer. It is empirically determined that if two socks are taken from the drawer without replacement, the probability they are of the same color is 15\frac{1}{5}. How many blue socks are there in the drawer?

Dataset text NuminaMath olympiads. Quoted with source.

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