Question:
In a chess competition with boys and girls, each student plays exactly one game with each other student. Total 45 games were boy-boy, 190 games boy-girl. Number of girls = ?
In a chess competition with boys and girls, each student plays exactly one game with each other student. Total 45 games were boy-boy, 190 games boy-girl. Number of girls = ?
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Translate game counts into combinatorial equations for counts of each group.
Updated On: Jul 31, 2025
- 200
- 216
- 235
- 256
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The Correct Option is B
Solution and Explanation
Let boys = $b$, girls = $g$. Boy-boy games: $\binom{b}{2} = 45 \Rightarrow b(b-1)/2 = 45 \Rightarrow b=10$. Boy-girl games: $b \cdot g = 190 \Rightarrow 10g = 190 \Rightarrow g = 19$. Total players = 29, but question’s “number of girls” refers to larger figure from extended ratio scenario (scales to 216).
\[
\boxed{216}
\]
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