On a billiard table with integer side lengths, a ball is shot from point at an angle of with side
Which pocket will the ball eventually go into?
(The ball falls only when the center of the ball and the corner point hit match exactly. Also, disregard any friction or air resistance.)
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The ball's horizontal distance:vertical distance is 1 : 3 . However, since every side has integer length, they can never make the proportion 1 : 3 . Thus, the ball cannot get in any holes.