In a chess tournament, each player plays against every other player exactly once

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

In a chess tournament, each player plays against every other player exactly 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: Identify the total number of players, which is 12 in this case.
Step 3: Use the formula for calculating the number of games played, which is n(n-1)/2, where n is the number of players.
Step 4: Substitute the number of players into the formula: n = 12, so we calculate 12(12-1)/2.
Step 5: Simplify the expression: 12 - 1 equals 11, so now we have 12 * 11 / 2.
Step 6: Multiply 12 by 11 to get 132.
Step 7: Divide 132 by 2 to find the total number of games: 132 / 2 equals 66.
Step 8: Conclude that the total number of games played is 66.

Combinatorial Counting – The problem tests the understanding of how to count unique pairings in a set, specifically using the formula for combinations.
Understanding of Tournament Structure – It assesses the knowledge of how round-robin tournaments function, where each player competes against every other player.