190Tutorial3

Tutorial 3

3. (Mindscape 14, Chapter 2.1 of the textbook). You have 10 pairs of socks, five black and five blue, but they are not paired up. Instead, they are all mixed up in a drawer. When you stumble out of bed early in the morning (to get to an early math lecture, which you could not possibly miss) you can't turn on the light in case you wake up your pet sheep who sleeps under your bed. So you start pulling socks out of the drawer in the darkness. How many socks must you pull out to guarantee that you have a pair of one colour? How many must you pull out to guarantee you get two pairs of socks? How many must you pull out to guarantee you get a black pair? Do you even care if your socks match?

There are 10 pairs of socks. 10 black Socks and 10 blue.

1. To guarantee you have two of one colour, you need to pull out three socks. This is because for any combination of three socks, it is impossible not to have two the same.
2. To guarantee you have two pairs of socks, you only need to pull out four socks. Since a pair consists of two socks, four socks makes two pairs. If you were concerned about colour however, you would need five socks to ensure you had two pairs of socks which match.
3. To be guarantee you get a black pair, you need to pull out at least twelve socks. Since there are 10 non-black socks, in a worst case, it is possible that all non black socks are drawn before a black sock is drawn.