Since the highest total score can be 120×36=4320 (minutes),

So the total score. A in a4 1b is less than 4.

36=4×9, so this total score can be divisible by both 4 and 9.

According to the characteristic that numbers can be divisible by 4 and 9 at the same time,

a=2，b=2。

That is, the total score is 24 12,

Then the average score is: 24 12÷2=67 (points).

A: The average score of each player is 67 points.