Mathematics Magazine for Grades 1-12
in a Bipartite
coach’s problem (a real problem for a real coach)
In a team sport ( football,
rugby, hockey) where n players go on
the field, the coaches of every team, together with their teams of experts,
manage to determine the risk a coach is taking by deciding that player i
) be put to play on the position j (
Having this information
within reach (a rectangular matrix with m lines and n columns,
), the coach has to naturally solve this problem:
This problem, although very
old, can now be solved very easily; even more, we now can rigorously explain why
a coach makes some changes that the spectators “do not understand” (for
example, when he replaces a forward with a mid-fielder or a defender).
Read more on the written version of the publication.