Question 172
Consider a chess tournament involving earthlings and aliens in which each player plays against every other player exactly once. At the end of the tournament, each player had obtained half of the points he won playing against earthlings and half playing against aliens. Letting $t$ and $a$ be the numbers of earthlings and aliens, respectively, answer:
a) What is the total number of games in this tournament, in terms of $t$ and $a$?
b) In this tournament, each win is worth 1 point, each draw is worth 0.5 point and each loss is worth zero points. What is the total number of points of the earthlings in terms of $t$ and $a$?
c) Verify that the total number of players in the tournament is a perfect square.
a) What is the total number of games in this tournament, in terms of $t$ and $a$?
b) In this tournament, each win is worth 1 point, each draw is worth 0.5 point and each loss is worth zero points. What is the total number of points of the earthlings in terms of $t$ and $a$?
c) Verify that the total number of players in the tournament is a perfect square.