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. $12$
• B. $15$
• C. $30$
• D. $36$

Answer 1

Answer: (B)

$15$

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