Correct Answer - Option 2 : 17
Let there be x players
1st player will play with x - 1 players twice = 2(x- 1 ) matches.
2nd player will play with x-2 players as with 1st player he has already played = 2( x-2) matches
So, total number of matches = 2(x -1) + 2(x- 2) + 2(x-3) + .......+2(2) + 2(1) + 2(0)
= 2 ( 1 + 2 + ..... + (x-3) + (x-2) + (x -1) )
= 2 (x-1)x/2
= (x-1)x
⇒x (x-1) = 272
⇒x (x-1) = 17 × 16
⇒x = 17
So, the number of players participated = x = 17
Hence, option 2 is the correct answer.