# Red socks and Blue socks

**Discrete Mathematics**Level 5

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?