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In the Reflecting Ball Game a ball can be launched from points 1, 2, 3, 4, 5 or 6 in the direction shown. When a ball hits a side of rectangle  it bounces at a  angle back into the playing field. The path of the ball ends when it hits a corner point A, B, C or D. The path for starting point 5 is shown in the diagram. Each of the 15 non-overlapping squares of the playing field measures 2 cm by 2 cm. What is the length of the longest possible path for a ball launched from a starting point?

 

 Apr 8, 2021
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The longest possible path is 20*sqrt(2).

 Apr 8, 2021

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