Probably just fairly bog standard geometry combined with some material science/engineering on the physical properties of the cardboard (such as how much it can compress/stretch)
Geometry: this problem more or less boils down to a 2d analysis since we need merely to look at a circular cross section. You could calculate the area each roll takes up by calculating the outer circle area minus the hole's area, then divide the hole area by the ring's area to get a theoretical maximum. This is assuming the material cannot stretch or compress. Not sure if this has a name, but it probably does.
Material science: Maybe you could measure the dimensions of a roll, stress test it in various ways, and re-measure the new dimensions to get a profile of how the cardboard warps. You could use that to get a better estimation of how much cardboard you can stuff into itself, but I'm not as sure on the details there.
My first long term partner taught me this trick, and consequently many little lessons on how to enjoy a life. Nice to see others appreciating the dull side of life.
I know you'd probably have an uphill battle with people that aren't used to it, but I wish my parents had started us on it when I was a kid. I picked up one of those nozzles you attach on the toilet supply line and hang from the side of the tank, and it was a game changer.
I always go back to that scene in Parks and Rec where Andy talks about wiping his ass being like it's a felt marker, it never seems to run out...
have you found the ones with different sized paper cores? one time a few years ago, i had one inside another inside a third, they just slid over each other.
Yup, that's why 12 became the limit. On my current one, I've made sure to kink that "tip" in the middle to allow for folding once I get to 9 or so, which is why I'm hoping my current one becomes the new record.