Question

A chess tournament was being held. This single-elimination tournament (in which paired competitors

played matches and only the winner of a match continued to the next round) began with 16 competitors.
How many matches were played?

A total of matches were played. _____

I really need help with this problem!

Answer 1

A total of 15 matches were played.

Explanation:

To determine the number of matches that were played in the chess tournament, knowing that there are 16 participants who face each other in a tournament of direct elimination, the following logical reasoning must be carried out:

In the first round there are 16 players, so being matches between 2 players, there are 8 matches (16/2). In the second round, applying the same reasoning and taking into account that there are only 8 players left, since the others have been eliminated, there are 4 matches (8/2). The same in the semifinals, where there are 2 games (4/2), and finally, the final to a single game.

Therefore, since 8 + 4 + 2 + 1 equals 15, the number of matches played in the tournament is 15.