BDMO 2019 national - junior/9

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
M F Ruhan
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BDMO 2019 national - junior/9

Unread post by M F Ruhan » Thu Apr 08, 2021 10:11 pm

In the cartesian coordinate system, four points (0, 0),(20, 0),(20, 19) and (0, 19) are used
as vertices to draw a rectangle. At first, a ball with negligible size is at the (0, 0) point. It then started
to move towards the point (2, 1). Every second, the ball passes the amount of distance between (0, 0)
to (2, 1). If it collides with one side of the rectangle, it follows the law of reflection and comes back
to the rectangle. If it collides with a corner, it again follows the law of reflection and comes back in
the direction it went in. Until the 2019th second, how many times will the ball collide with a corner point?

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