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Beam Of Light

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 2times2, 2times6, 2times10, 2times14, ... , 2times50, 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, 3timesk, 4timesk, et cetera.

Problem ID: 62 (Jan 2002)     Difficulty: 1 Star

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