When a single particle is fired at the double-slit wall, does it always go through both slits at the same time, or does it sometimes just hit the wall? I'm wondering because I'm trying to wrap my head around what counts as an interaction. If the particle goes through both slits all the time then it doesn't seem to be interacting with the wall, but if it goes through both slits only sometimes, then it must be interacting with the wall, in which case the wave function collapses into either "hit the wall" or "going through both slits".

The transmission will depend on how much open area you have, so "hit the wall" is certainly an option. The observation of inetrference is made only on those that pass through, not on the ones that hit. Going through the slits still leaves you with a particle that can interfere with itself.

Right. Makes sense.