Final answer:
The Pigeonhole Principle demonstrates that in a 16-team soccer tournament, at least two teams will have played the same number of matches.
Explanation:
Mathematically, in a soccer tournament with 16 teams where every pair of teams must compete against each other, it can be proven that at any point during the tournament, there are at least two teams that have played the same number of matches.
This can be shown using the Pigeonhole Principle. Since each team plays against every other team, in a tournament with 16 teams, there will be a total of 15 matches for each team. If we consider the number of matches played by each team ranging from 0 to 15, by the Pigeonhole Principle, at least two teams must have played the same number of matches.
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