Comment by logicallee

yes this is correct. Thanks for writing that out, it's really interesting to read how you solved this without picturing it.

It's a bit surprising to me that it was unclear what I meant by horizontal/level, I thought this word is well-known and easy to understand. Here's what I mean by horizontal: For me, it means that with respect to the ground, the ray isn't rising or falling as it travels, i.e. it's level (like a plane flying in level flight with respect to the ground, not rising or falling). This constraint doesn't really matter I guess, except that I said that the cube is also level on the ground on one of its surfaces, so since you have to cast the ray in a horizontal/level way, you can't cast the ray at an angle through one of the corners so it goes through the opposite corner of the cube, since - if you think of the ray like a plane - you can only move the angle of the ray side to side not up and down, it stays in level flight = horizontal, so you can't cast it through both opposite corners if the cube is lying flat on the horizontal on one of its surfaces. As I just wrote this paragraph, I pictured what my description of casting through both corners the would look like and why it's not level with the ground anymore. I guess it's harder to follow my words without picturing it.

You mentioned it's not clear how being horizontal constrains the ray, based on what I wrote and what I meant about it being level, is it now clearer how this constrains some of the rays that can be cast? (Like how you can't cast a ray through the opposite ends of the cube now)? Or is that hard for you to follow? For me I think maybe my words could be written in a bit confusing way but I think someone can understand them if they can picture what I referred to. Without that mental picture it could be difficult though.