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 More bouncing (Posted on 2016-03-09)
Place an isosceles right triangle with its right angle at the origin and legs along the positive x- and y-axes.

Imagine this triangle is three mirrors and a laser is fired from the origin with some positive slope.

The laser will bounce around and one of 3 possibilities will occur:
1. The laser will eventually come back to the origin.
2. The laser will eventually hit one of the other corners.
3. The laser will never hit any of the corners.

For a given slope, how can you tell which will happen?

 No Solution Yet Submitted by Jer No Rating

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 re: proposed solution | Comment 2 of 3 |
(In reply to proposed solution by Charlie)

I agree with your analysis except for one thing: You state the numerator or denominator needs to be a power of 2 to hit a corner other than the origin.  That should be a multiple of 2 instead.  Consider slopes of 5/6, 7/10, 3/14, etc.
 Posted by Brian Smith on 2016-03-10 00:00:24

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