A group of players play a game in which each player contributes an amo

X = money one person contributes = number of the game
Winning a game, he gets X^2 - X
(subtract his contribution from the winning amount)
If he loses, the money will be -X

He wins half the number of games and loses half after X rounds
(X^2 - X) * X/2 + (-X) * X/2 = 4X
X^3 - 2X^2 = 8X
Because X can not be 0 so
X^2 - 2X = 8
X^2 - 2X + 1 = 9
(X-1)^2 = 9
X>0 so X = 4

The answer is B

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Let's denote the number of players in the group by n.

Each player contributes an amount equal to the number of players in the group, so each player contributes n units of money. Since there are n players, the total amount of money collected for each game is n×n=n2 units of money. The winner of each game gets this entire amount as the prize money.

The number of times they play this game is equal to the number of players in their group, so they play n games. If a player wins half the number of games, then he wins 2n games.

The total prize money this player wins is 2n×n2=2n3 units of money.

Since each player contributes n units of money for each game, and there are n games, the total amount of money this player contributes is n×n=n2 units of money.

The profit earned by this player is the total prize money earned minus the total amount of entry fees paid, which is 2n3−n2.

According to the problem, this profit is four times the money he contributed for each game, which is 4n units of money. Therefore, we have the equation:

2n3−n2=4n

n3−2n2=8n

We factor out the common term n:

n(n2−2n−8)=0

We then factor the quadratic expression n2−2n−8:
n(n−4)(n+2)=0

This gives us three possible solutions: n=0, n=4, and n=−2. Since n represents the number of players in the group, it must be a positive integer. Therefore, we discard n=0 and n=−2, leaving us with:
n=4
Thus, the number of players in the group is 4.

4 player need to contribute total 16 in one game.
for 4 game one need to contribute 16 and he can earn 2X16 by winning in two game.
playing 4 game, but failing in 2 and winning in 2, net earning is (2X16-16)=16, which is four times of per game contribution of one player.
So, Ans:B