PICKING TEAMS

Keep it fair with a strategy that relies on geometry.

- BY IVARS PETERSON

You and some friends are planning an afternoon of soccer scrimmages. There are eight of you, so you can play in teams of four. You want to play enough games so that each player gets to play with everyone else. And, to be fair, you would like each pair of friends to be teammates the same number of times.

How would you choose the teams and decide how many games to play?

One way to try to solve the problem is to pick the teams randomly. You could have four blue and four red slips of paper in a box. Then, at the start of a game, each player would reach in without looking and pull out a slip. Someone who picked red would join the red team.