Six Shoes and Twenty-Four Socks

The Problem

You are in the dark, and on the floor there are six shoes of three colors, and a heap of twenty-four socks, black and brown. How many socks and shoes must you take into the light to be certain that you have a matching pair of socks and a matching pair of shoes?

The Solution

Let c := the number of colors of socks and h := the number of colors of shoes. The number of shoes you have to take into the light is h + 1 (which is 4). The number of socks you have to take into the light is c + 1 (which is 3).