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In a recent chess tournament, each player played against every other player exac

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Question: In a recent chess tournament, each player played against every other player exactly once. If there were 10 players in total, how many games were played? (2023)

Options:

  1. 45
  2. 90
  3. 100
  4. 50

Correct Answer: 45

Exam Year: 2023

Solution: 

The number of games played in a round-robin tournament is given by the formula n(n-1)/2, where n is the number of players. Here, n = 10, so the number of games is 10(10-1)/2 = 45.

In a recent chess tournament, each player played against every other player exac

Practice Questions

Q1
In a recent chess tournament, each player played against every other player exactly once. If there were 10 players in total, how many games were played? (2023)
  1. 45
  2. 90
  3. 100
  4. 50

Questions & Step-by-Step Solutions

In a recent chess tournament, each player played against every other player exactly once. If there were 10 players in total, how many games were played? (2023)
  • Step 1: Identify the total number of players in the tournament. In this case, there are 10 players.
  • Step 2: Understand that each player plays against every other player exactly once.
  • Step 3: Use the formula for calculating the number of games in a round-robin tournament, which is n(n-1)/2.
  • Step 4: Substitute the number of players (n) into the formula. Here, n = 10.
  • Step 5: Calculate (10 - 1), which equals 9.
  • Step 6: Multiply 10 by 9 to get 90.
  • Step 7: Divide 90 by 2 to find the total number of games played, which equals 45.
  • Combinatorics – The question tests the understanding of combinations, specifically how to calculate the number of unique pairs (games) that can be formed from a set of players.
  • Round-Robin Tournament Structure – It assesses knowledge of tournament formats where each participant competes against every other participant exactly once.
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