Red socks and Blue socks

A drawer contains a mixture of red socks and blue socks, at most 1950 in all. It so happens that, when two socks are selected randomly without replacement, there is a probability of exactly \(\frac{1}{2}\) 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?


Image Credit: Flickr Alison Clayton.
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