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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 $ABCD$, it bounces at a $90^{\circ}$ angle back into the playing field. The path of the ball ends when it hits 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 has an area of $2$ square centimeters. What is the length of the longest possible path for a ball launched from a starting point?

 Mar 8, 2021
 #1
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You can compute the path for each point:

 

1: 12 sqrt(2)

2: 24 sqrt(2)

3: 30 sqrt(2)

4: 16 sqrt(2)

5: 10 sqrt(2)

6: 20 sqrt(2)

 

So the longest path is 30 sqrt(2)

 Mar 8, 2021
 #2
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its wrong :/

Guest Mar 11, 2021

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