There are $$10$$ players, so there are $$10\times9\div2=45$$ games in total. The sum of the points of two players in each game must be $2$. Thus, the sum of all points earned by $10$ players in $45$ games is $2\times45=90$. 
A chess singles tournament had $10$ players. Each player played with every other player only once. $2$ points are earned for winning a game, $0$ points are earned for losing a game, and $1$ point is earned by each player in a tie. After the tournament, the judge finds that the sum of these $10$ players\textquotesingle{} points is~\uline{~~~~~~~~~~}~. 
$$180$$ 
$$100$$ 
$$50$$ 
$$20$$ 
$$90$$ 