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Question

In a chess tournment, where the participants were to play one game with another. Two chess players fell ill, having played 3 games each but not with each other. If the total number of games played is 84, the number of participants at the begining was

A
15
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B
16
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C
20
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D
21
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Solution

The correct option is B 15
Suppose the two players did not play at all so that the
remaining ( n-2) players played (n22) matches
Since these two players 3 matches each
Hence , the total number of matches is
(n22)+3+3=84
(n1)(n2)1.2=78
n25n+6=156
n25n150=0
On solving this , we get
n = 15
Hence , the number of participants at the beginning was
= 15

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