Does anyone else think that posing this problem to kids studying arithmetic is insane? It is the kind of problem that discourages kids from learning math because it has no obvious relationship to any practical problem and because it is extremely difficult to solve with the mathematical tools that the child presumably has. Although it can presumably be solved through pure logic without any algebraic notation, such a solution is not easy. It's not that obvious using basic algebra plus logic.
A beat B, C, and D. 3 wins is odd number of wins above 0 and below 5.
B beat C and E. 2 wins. 0 < 2 < 5.
C beat D. 1 win against a player with only 1 win. 0 < 1 < 5.
D beat B. Only 1 win. 0 < 1 < 5.
E beat A, C, and D. 3 wins, same as A. 0 < 3 < 5.
F beat A, B, C, D, and E. 5 wins and 5 + 2 = 7.
I solved it using a logic tree and algebra. It took a while.
EDIT By the way I did NOT prove that this solution was unique. At the beginning of the logic tree I was faced with a = 3 or
a = 1. My intuition suggested that a = 3 was more promising. I never explored the a = 1 branch. To show that there is a unique solution would require following every branch of the logic tree to its end to find a solution or a contradiction.
