Your sock drawer has 10 blue socks, 16 red socks, and 12 white socks. If you reach into the drawer in the dark, how many socks do you need to pull out to be sure you have a matching pair?

I can't figure out.

There are three colours in all, blue, red, and white.

Therefore the maximum you can get without getting a pair is three.

In the worst case, how many socks do you need to pull to get a pair?

To determine the minimum number of socks you need to pull out to be sure you have a matching pair, you need to consider the worst-case scenario. In this case, you would need to assume that the first socks you pull out are all different colors.

To solve the problem, you can use a concept known as the Pigeonhole Principle, which states that if you have more items than the number of groups you can put them into, at least two of the items must belong to the same group.

In this case, you have three different colors of socks: blue, red, and white. To be sure you have a matching pair, you need to pull out enough socks to cover all the possible combinations of colors. The worst-case scenario is that you pull out one sock of each color before getting a matching pair.

So, you would need to pull out a total of 3 + 1 = 4 socks to be sure you have a matching pair. The first three socks cover all the possible color combinations, and the fourth sock would complete a matching pair.

Therefore, to be sure you have a matching pair when reaching into the drawer in the dark, you need to pull out a minimum of 4 socks.