One of your dresser drawers contains 10 black socks and 10 blue socks. Suppose it is dark and you can’t tell what color a sock is when you look at it. If you start taking socks randomly one at a time from the drawer, how many would you have to take to guarantee that you get a matched pair, regardless of the color?
To guarantee that you get a matched pair of socks, regardless of the color, you need to consider the worst-case scenario. In this case, the worst-case scenario would be if you keep picking socks of different colors each time.
So, let's think about the maximum number of socks you can pick without getting a matched pair. In the first pick, you can choose any of the 20 socks. In the second pick, you need to pick a sock of a different color than the previous one, so you have 19 remaining socks of the opposite color. In the third pick, you again need to pick a sock of the opposite color, so you have 18 remaining socks. This pattern continues until you have picked all 19 socks of one color, leaving only the remaining 1 sock of the opposite color.
Therefore, to guarantee a matched pair of socks, you would need to pick at least 20 + 1 = 21 socks from the drawer.