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Geometry Level 4

I have a box with dimensions $2 \times 51,$ and the insides of all its sides are covered with mirrors. From corner $A$ , I shoot a laser beam at $45 ^ \circ$ angle to side BC. Which corner would the laser beam come out of?

A B It would not hit any corner D C

1 solution

Aryaman Maithani
Jun 8, 2018

Let the diagram be described in terms of co-ordinates:

$A\equiv (0, 0); B\equiv (0, 2); C\equiv (51, 2); D\equiv (51, 0)$

During its rightwards journey, it can be seen that the light will hit the following points:

$(0, 0), (4, 0), (8, 0) \dots (48, 0)$

After hitting $(48, 0)$ , it will hit the following points:

$(48, 0) \to (50, 2) \to (51, 1)$ after which will begin its leftwards journey.

$(51, 1) \to (50, 0) \to (48, 2) \to (46, 0) \dots \to (2, 0) \to (0, 2) \equiv \boxed{B}$

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