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Question

There are 2 women participating in a chess tournament. Every participant played 2 games with the other participants. The number of games that the men played between themselves exceeded by 66 as compared to the number of games that the men played with the women. If the number of participants is k then the value of k6 is

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Solution

There are 2 women and let number of men are n
Then number of games played by men between themselves is 2( nC2)
Number of games that the men played with the women is 2(2n).
According to question :
2( nC2)2(2n)=66
2.n(n1)24n=66
n25n66=0(n11)(n+6)=0
n=11(n>0)
Hence total participants(k)=2+11=13
k6=7

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