mathschallenge.net

Problem

If a light beam is fired through the top left corner of a 2 by 3 rectangular prism block at a 45 degrees towards the opposite wall, it will emerge from the top right corner.

If the light bounces around a 2 by 4 rectangle, it emerges from corner D.

If a beam of light is fired through the top left corner of a 2 by 50 rectangle, which corner will it emerge from?

Solution

Consider the two diagrams.

   

It can be seen from this that rectangles measuring 22, 26, 210, 214, ... , 250, that is, even non-multiples of 4, will finish in the bottom right corner, C.

Will the light ever return to A?
Investigate other size grids, 3k, 4k, et cetera.