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.
Since there are only 3 colors of socks, the fourth pick is sure to give you a matching pair.
496
There are 3 different colors, so regardless of how many there are of each one, even if worst case scenario, you take out a blue sock first, then a red one and then a white one, the next color has to be one of them, so you would have a pair, so the answer is 4
But what if you pull out four of one color socks?
Socks are dumb
it’s 4 my teacher said it is
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 want to ensure that no matter which socks you pull out, you will always have a matching pair.
The worst-case scenario occurs when you initially pull out all the socks of a color that has the least number of socks in the drawer. In this case, the color with the smallest number of socks is white, with 12 socks.
So, to guarantee a matching pair, you need to pull out the maximum number of socks from the other colors until you have more than 12 socks. Since there are 26 socks in total between blue (10) and red (16), you will need to pull out at least 13 socks to be certain of having a matching pair.
Therefore, the minimum number of socks you need to pull out to be sure you have a matching pair is 13 socks.