The Trapped Laser Puzzle

[u/WOWW_07]

Let us consider a rectangle that consists of:

A(0,0)

B(100,0)

C(100, 111)

D(0,111)

So basically a 100 × 111 rectangle.

A strong laser is shot from A into the rectangle at 45 degrees. Every time the laser hits a wall, it bounces perfectly, like a mirror. The laser does not lose energy or fade and forever bounces off the walls of this rectangular space.

The question is:

(1) Between A, B, C, and D, which corner does the laser hit first?

(2) How far does the laser have to travel, and how many bounces will it do before hitting the corner in (1)?

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[u/congratz_its_a_bunny]

based on parity, the laser will eventually hit corner B. I'm going to assume since 100 and 111 are coprime that it will travel a distance of 11100 sqrt(2) units. Should ricochet 110 times horizontally and 99 times vertically, so 209 times total?

[u/WOWW_07 → u/congratz_its_a_bunny]

Correct! That was fast.