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

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Question: In a chess tournament, if each player plays against every other player exactly once, and there are 10 players, how many games are played?

Options:

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

Correct Answer: 45

Solution: 

The number of games played is given by the combination formula n(n-1)/2. For 10 players, it is 10(10-1)/2 = 45 games.

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

Practice Questions

Q1
In a chess tournament, if each player plays against every other player exactly once, and there are 10 players, how many games are played?
  1. 45
  2. 50
  3. 90
  4. 100

Questions & Step-by-Step Solutions

In a chess tournament, if each player plays against every other player exactly once, and there are 10 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 10 players, we need to find out how many unique pairs of players can be formed.
  • Step 3: Use the combination formula to calculate the number of unique pairs. The formula is n(n-1)/2, where n is the number of players.
  • Step 4: Substitute the number of players (10) into the formula: 10(10-1)/2.
  • Step 5: Calculate 10-1, which equals 9.
  • Step 6: Multiply 10 by 9, which equals 90.
  • Step 7: Divide 90 by 2, which equals 45.
  • Step 8: Conclude that there are 45 games played in total.
  • Combinatorics – The problem involves calculating the number of unique pairs (games) that can be formed from a set of players.
  • Combination Formula – Understanding the use of the combination formula n(n-1)/2 to determine the number of games played in a round-robin format.
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