2023 WSMO Speed Round Problems/Problem 3

Problem

There are 6 pairs of socks for each color of the rainbow (red, orange, yellow, green, blue, indigo, violet) in a sock drawer. How many socks must be drawn from the drawer to guarantee that a pair of red socks have been drawn?

Solution

There are $6\cdot2\cdot6 = 72$ non-red socks. Thus, a pair of red socks is guaranteed after $72+2 = \boxed{74}$ socks have been drawn.

~pinkpig