Well, they went down the sink as far as I know because we had to shave in the bathroom. See, the razors they gave us were single blades which were serrated, basically, and the shaving cream was what I called "Old Guy Plus" (hydrochloric acid). And shaving my whole beard when it's full with a single/double blade is like trying to saw through the top of a maximum security prison's barbed-wire fence with a yo-yo string, so yes, pain ensued, bumps, redness, and all. Never nicked myself, though.
After shaving there I felt like was 8 years old and completely naked. I also felt drafts just from walking and my face would generally feel way, way colder.