Question 167
In chess tournaments, usually each win is worth 1 point, each draw 0.5 point and each loss zero points. In the "Magistral Championship" of chess only International Masters (IMs) and Grandmasters (GMs) took part. The number of GMs was ten times the number of IMs. Each chess player played only once against every opponent, and so, if $n$ was the number of players, then $\frac{n(n-1)}{2}$ games took place. The sum of the points of all the GMs was 4.5 times the sum of the points of all the IMs. That said, we ask:
a) How many International Masters took part in this competition?
b) How many Grandmasters took part in this championship?
c) How many games did the tournament have?
a) How many International Masters took part in this competition?
b) How many Grandmasters took part in this championship?
c) How many games did the tournament have?