It works the other way, the shooter position is fixed as well as your position. Your are allowed to place a finite amount of blockers to make your position safe. The video comment say that it is always possible to make your place safe with at most 16 blockers. There is a link to the actual code used.

Does this also work in a 3D environment?

Yes, but you'd need up to 64 obstacles.

does it work in a 1D environment? yes, 1 blocker.

does it work in a 4D environment?

Sure, a time blocker that is placed before the laser is ever turned on.

This video explains it. His pinned comment explains the mod arithmetic:

https://www.youtube.com/watch?v=jJ6FD59U0_E

I wish he had explained the mod arithmetic more, the periodicity of 4 is really at the heart of the solution.

Thanks for the share! I took some quick (read, not proof-read) snippets on this if anyone wants to see: https://synth.app/s/uiElJvnnk

You could try projecting rays from start through the obstacles to see where they intersect after a limited number of reflections. This should narrow it to a few candidate spots

I'm curious why you couldn't just surround yourself with the 16 objects. Perhaps they're meant to be much smaller than the person?

The posted solution seems to work even when the objects have zero area, and are just points in space. If you just surrounded the target with 16 points, there would either be gaps or the points would be infinitesimally close to the target and would occupy the same space.

So that means that any possible laser coming out of the shooter's position eventually passes through one of these 16 specific infinitesimally small points _before_ ever hitting the target? And that is always possible for any position of shooter and target? That's bonkers, wow.

Both person and obstacles are meant to be infinitesimally small, i.e. points with mass zero, which makes one really appreciate the beauty of the solution.

This way allow you to hide. A tight group of obstacles will give away your position and it will be demolished with a bazooka. Though an attacker might calculate the possible location of your body and use a grenade. But it might be unsafe for himself.

There isn't always a safe spot, but you can generate a room that makes a safe spot- https://www.youtube.com/watch?v=jJ6FD59U0_E

The area covered by the lasers should remain painted, so we could see all the spots which haven’t been hit ever.