Respuesta :
Two teams have the same number of played games.
What is pigeonhole Principle?
- The pigeonhole principle is one of the simplest but most useful ideas in mathematics, and can rescue us here.
- \A basic version says that if (N+1) pigeons occupy N holes, then some hole must have at least 2 pigeons. Thus if 5 pigeons occupy 4 holes, then there must be some hole with at least 2 pigeons.
- If n + 1 or more pigeons occupy n pigeonholes, there will be more than one pigeon in at least one pigeonhole.
Suppose that there are n football teams in the tournament.
The number of games for a team is either 1 or 2 or 3 . . . or (n – 1). These (n – 1) numbers correspond to (n – 1) pigeonholes in which the n teams are to be housed. So at least two of them should be in the same pigeonhole.
Therefore, At some moment, two teams have the same number of played games.
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