Each participant must start from each starting position and encounter every other participant. This is a common problem in sports tournaments, where it is desirable for each player to play against every other player at least once and try all available tracks.
The calculator uses a greedy algorithm that may not provide an optimal solution. Finding optimal solutions for these types of combinatorial problems, such as the "schoolgirls problem" or "social golfers problem," is computationally challenging and falls under NP-complete problems. However, solutions for some special cases are known and published.