So I'm a bit confused as to how a single gear rotation comes about.

I noticed that while rotating all gears simultaneously, a rotation of 1 on a large gear rotates all of the small gears one as well, leading to a +4 total rotation. If one rotates it again, this leads to a +8 (or +3) rotation on the small gears.

Is this how the single gear rotation comes about? Or am I missing something?

By this logic, though, shouldn't it be impossible to get a +1 rotation on a large gear (except without a +1 on a small gear, I think)?

Or, perhaps this is the whole trick to solving it and I'm two steps away from figuring it out?



Also a mechanism question: Is it likely to wear out?

It's because the number of teeth is odd - rotating a single gear with five teeth six teeth counterclockwise winds up rotating it one tooth clockwise.

For the large gears, think about the total number of teeth they'll all rotate together. Whenever you rotate a single half one tooth there are two big gears which rotate one unit, so the sum of the rotations over all big gears will always be even.