Do you know about Chess tournaments?

Probability Level 3

A certain number of students of a school have participated in a chess tournament of their Annual Sports Meet. It was found that in 105 games both the players were girls and in 300 games both the players were boys. The number of games in which boy and girl played against each other are?

The answer is 375.

2 solutions

Hs N
Sep 9, 2014

In a competition with $n$ participants, where each player plays each opponent exactly once, the number of games played equals the $n-1$ th triangle number. The same is true, if we split off the boys-only and girls-only parts of the tournament.

Since there are $105=1+2+\ldots+14$ girls-only games, it thus follows there are 15 girls involved in the tournament. Similarly, there are $25$ boys involved. Since every boy plays exactly once against each girl, the number of girl-boy matches thus is $25\cdot15=375$ .

Don't love this question, it's very unclear that it's a round robin tourney

Bradley Jackson - 6 years, 8 months ago

Yes you are right.Its not mentioned clearly.

rahul saxena - 6 years, 2 months ago

Is this right too?

For the girls, if there were $n$ games, then ${n \choose 2}=105$ which gives us $n=15$ .

Similarly, for the boys, $n=25$ and hence the answer is $15 \times 25 = 375$ .

Omkar Kulkarni - 6 years, 4 months ago

Varun Narayan
Sep 11, 2014

suppose n girls and m boys are so total game s =m n
nC2=105 so n=15 and mC2=300 so m=25 . final ans =m
n=375

Do you know about Chess tournaments?

The answer is 375.

2 solutions

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