Mr. Sockem wears only black or navy blue socks, which are exactly alike except for their color. He has six pairs of each color, and he keeps them all mixed up in a drawer. One night, while the room was in complete darkness, he wanted to find a pair of matching socks. How many socks must he remove from the drawer to be sure he has a pair that match?
How do you solve this question?
To solve this question, we need to find the minimum number of socks Mr. Sockem must remove from the drawer to be sure he has a pair that match.
Since Mr. Sockem has six pairs of each color (black and navy blue), we can start by assuming the worst-case scenario. That is, he picks socks of different colors each time he removes one from the drawer. In this case, he would need to remove at least 13 socks to be sure he has a matching pair.
Here's the step-by-step breakdown:
1. The first sock he removes could be either black or navy blue, so there is no matching pair yet.
2. The second sock he removes could be of the opposite color from the first one, so there is still no matching pair.
3. If he continues in this manner, removing socks of alternating colors, he would need to remove six socks of one color (let's say black in this case) before the seventh sock he removes will be a matching pair.
4. However, there is also a possibility that he might have already found a pair of matching socks before reaching the sixth black sock.
5. So to be completely sure, he needs to remove the remaining six navy blue socks, as well. In this worst-case scenario, he will need to remove a total of 6 black + 6 navy blue + 1 more sock (the seventh black sock).
Hence, the minimum number of socks Mr. Sockem must remove from the drawer to be sure he has a pair that match is 13 socks.