It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least two socks of the same color?
2
3
24
25
47
48
This is a classic pigeonhole principle problem. With only 2 colors available, if you pick 3 socks, you are guaranteed to have at least 2 of the same color. The worst case is picking 1 red and 1 blue first, then the third sock must match one of them.
To solve this problem, we can use the concept of the Pigeonhole Principle. The Pigeonhole Principle states that if you have n+1 objects to distribute among n boxes, then at least one box must contain more than one object.
In this case, we have two colors of socks (red and blue) and we want to find the minimum number of socks we need to take from the drawer to ensure that we have at least two socks of the same color.
Since we have 24 red socks and 24 blue socks, the worst-case scenario is that we first take one red sock and one blue sock. We don't have two socks of the same color yet, so we need to take one more sock.
At this point, we can be sure that we have at least two socks of the same color, regardless of the color of the third sock we take. Therefore, the minimum number of socks we need to take from the drawer to get at least two socks of the same color is 3.
Therefore, the correct answer is B) 3.