We have 10 teams. Each team will play against every other team, alternating home and away stadiums. How would you design a schedule for these matches?

A common approach is to use a round‑robin schedule. For an even number of teams (10), create a list of teams and fix one team in position 1. Rotate the remaining teams clockwise each round. For round r, pair team i with team (n-i+1) where n is the number of teams. This yields 9 rounds, each team playing 9 matches. To alternate home and away, assign the fixed team as home in odd rounds and away in even rounds, or flip the home/away status for each pair in successive rounds. The algorithm runs in O(n^2) time and produces a balanced schedule with no team playing more than once per round. If you need to avoid consecutive home or away games, you can add a simple post‑processing step that swaps venues for conflicting pairs.