Question

$8$ players compete in a tournament, every one plays everyone else just once. The winner of a game gets $1$, the loser $0$ or each gets $\frac{1}{2}$ if the game is drawn. The final result is that every one gets a different score and the player playing placing second gets the same as the total of four bottom players.The total score of all the players is

• A. $28$
• B. $21$
• C. $20$
• D. $22$

Answer 1

The correct option is A $28$

The players get $1$ for winning

and $\frac{1}{2}$ for a draw

So the sum of points of the players for one match is $1$

Hence the total score for ${}^8{C}_2=\frac{8\times 7}{2}$ matches is $28$

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