Question

You have ten pairs of socks, five blue and five black. How many socks μst you pull out to guarantee that you have one

a) Blue sock
b) Black sock
c) Matching pair of socks
d) Different-colored pair of socks

Answer 1

To guarantee having a blue sock, black sock, a matching pair, or a different-colored pair of socks, you will need to pull out a maximum of six, six, three, or three socks respectively, due to the possibility of worst-case scenarios.

Step-by-step explanation:

The question involves determining the minimum number of socks that need to be pulled out from a group consisting of ten pairs of socks, five blue and five black, to guarantee a certain outcome. Here are the step-by-step solutions for each case:

1. To guarantee one blue sock, you need to pull out at most six socks. The worst-case scenario is pulling out all five black socks before getting a blue one.
2. Similarly, to guarantee one black sock, you need to pull out at most six socks, for the same reason as the first case.
3. To guarantee a matching pair of socks, you need to pull out at most three socks. Pulling out two socks of one color will always leave you with at least one pair.
4. To get a different-colored pair of socks, you must pull out at most three socks. After pulling out two socks of the same color, the third sock will either be the same color, giving you a matching pair, or a different color, giving you a pair of different colors.