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There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is:
- 12
- 9
- 7
- 11
Correct answer: 12
Solution
The number of games played among the men is given by the combination formula for pairs of men, multiplied by 2 since each pair plays two games. The games played between men and women is simply twice the number of men times the number of women. Setting up the equation based on the problem statement and solving for m leads to the conclusion that m equals 12.
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