In a chess tournament, each player plays every other player once. If there are 1

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Question: In a chess tournament, each player plays every other player once. If there are 12 players, how many games are played?

Options:

Correct Answer: 66

Solution:

The number of games played is given by n(n-1)/2. For 12 players, it is 12(12-1)/2 = 66 games.

In a chess tournament, each player plays every other player once. If there are 12 players, how many games are played?

In a chess tournament, each player plays every other player once. If there are 12 players, how many games are played?

Step 1: Understand that each player plays against every other player exactly once.
Step 2: Recognize that if there are 12 players, we need to find out how many unique pairs of players can be formed.
Step 3: Use the formula for combinations to find the number of unique pairs: n(n-1)/2, where n is the number of players.
Step 4: Substitute 12 for n in the formula: 12(12-1)/2.
Step 5: Calculate 12-1, which equals 11.
Step 6: Multiply 12 by 11 to get 132.
Step 7: Divide 132 by 2 to find the total number of games: 132/2 = 66.
Step 8: Conclude that there are 66 games played in total.

Combinatorics – The problem involves calculating combinations, specifically the number of ways to choose 2 players from a group of 12 to form a game.
Graph Theory – The scenario can be represented as a complete graph where each player is a vertex and each game is an edge connecting two vertices.