You are about to leave for vacation, but you forgot your socks! You go back to your room but lights are out, can't see. You remember that in your draw you have 10 pair black, 10 pair white and 11 pair blue all mixed up. How many socks do you need to take out to be SURE you have at least one matching pair?
there are only 3 colors, so the 4th sock must match one of the first three.
To determine the minimum number of socks you need to take out to be sure you have at least one matching pair, you can apply the concept of the Pigeonhole Principle. The Pigeonhole Principle states that if you have n+1 objects to distribute into n containers, then at least one container must contain more than one object.
In this case, think of each color of sock (black, white, and blue) as a container, and the socks as objects. Since you want to be sure you have at least one matching pair, you need to ensure that you have taken out enough socks to cover all possible combinations of colors.
To determine the minimum number of socks you need to take out, consider the worst-case scenario, which is that you keep drawing socks of different colors until there are no more unique colors left. This means that you would need to take out one more sock than the total number of different colors.
In your case, you have 3 different colors of socks (black, white, and blue). So taking into account the worst-case scenario, you would need to take out 3 + 1 = 4 socks to be sure you have at least one matching pair.
So, the minimum number of socks you need to take out is 4.