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Question

In a chess tournament each of six players will play with another players exactly once. How many matches will be played during the tournament ?

A
12
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B
15
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C
30
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D
36
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Solution

The correct option is A 15
The situation in which the matches will be played would be as follows :
(i) 1st player will play matches with other 5 players
(ii) 2nd player will play matches with 4 players other than the 1st player
(iii) 3rd player will play matches with 3 player other than 1st and 2nd players.
(iv) 4th player will play matches with 2 players other than 1st 2nd and 3rd players.
(v) 5th player will play match with 6th player only.
Therefore, the number of matches played during the tournament is
=5+4+3+2+1=15.

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