# Swimmers' Dilemma

One of my colleagues was on a master’s men’s swim team that set a world record in the 400-meter medley. He pointed out how the rules generate the complexities of creating the best team. The team members’ ages must sum to at least 200 years. Assuming each person’s time slows at an accelerating rate, you might think that minimizing the relay team’s time would require having each member be age 50. Yet my colleague is 53, but he is an exceptionally fine swimmer, especially at freestyle, which he swam in the meet. Having him on the team doesn’t slow the total time very much (he’s never the best among masters in any event); but including him allows the team also to include a 47-year-old who has several individual world records.
The programming problem becomes even more complex because each swimmer’s time slows at a different rate in different events. Since teams need time to practice, constructing the optimal team requires taking into account the sum of ages constraint, the current time of each potential team member in each relay leg, and the rate at which times are slowing for each person in each event. (HT: MS)