Problem: Shirts numbered consecutively from 1 to 20 are worn by 20 members of a bowling league. When any three of these members are chosen to be a team, the league proposes to use the sum of their shirt numbers as the code number for the team. Show that if any eight of the 20 are selected, then from these eight one may form at least two different teams having the same code number. Explain your answers and provides examples.