Exercise 10. I have socks of two different colors: 6 blue socks and 6 red socks. I take several socks at random. How many should I take, at a minimum, to be sure of having two socks of different colors?
Solution to Exercise 10: I must take, at a minimum, 7 socks to be sure of having two socks of different colors. Indeed, if I take 6 socks or fewer, it is possible that these socks are all blue. Conversely, if I take 7 socks, they cannot all be blue (so I will have taken at least one red sock), and they cannot all be red either (so I will have taken at least one blue sock). Thus, I will have taken two socks of different colors.