Solution
The Sock Drawer
Show the problem again
A drawer contains red and black socks. When two socks are drawn at random without replacement, the probability that both are red is exactly 1/2. What is the smallest possible number of socks in the drawer?
Worked solution
The answer is 4 (three red, one black). With r red socks out of n total, we need [r(r−1)] / [n(n−1)] = 1/2. Testing small cases: r = 3, n = 4 gives (3·2)/(4·3) = 1/2. No smaller n works, so the minimum is 4 socks. (The general solutions relate to Pell's equation; the next is 21 socks with 15 red.)
Source: Classic pigeonhole-principle exercise in wide circulation. Statement written for AxiomIQ.