The Sock Drawer

A drawer contains red socks and black socks. When two socks are drawn at random, the probability that both are red is 1/2.

(a) How small can the number of socks in the drawer be?

(b) How small if the number of black socks is even?

Suggestions

This is your first session working as a team and we hope you will have four sessions to work together, so you don't have to rush. Don't share personally identifying information but feel free to share interests and get to know each other a little. Explore the whiteboard. There are some interesting tools that can be very helpful when doing math such as the textboxes and the arrows (references) to point to chat messages or to the whiteboard.

The goal for this "Spring Fest" is for groups to do math together by discussing everyone's ideas, sharing interesting math questions that you think of and exploring these well as a team. We are not grading you or judging how smart you are. This is for you to have fun doing math together. We encourage you to not just try to get a quick answer, but think about different approaches and explore different ideas in the group. There will be a place later on a wiki for you to publish your group's approaches.

After each session we can help share your group's ideas with other groups. You can learn from them and compare if you want. If you have time to give a nice summary of your insights, unanswered questions, and solutions in the "Summary" tab of your chat room, it will be easier for others to give you feedback or advance your ideas further.