Well the main point the old man makes IS interesting, and that's the part he sums up on the whiteboard. By taking the balls back up closer to the center of the wheel, there is always more weight on the outer opposite side to keep the wheel going. ...
That had me stumped for a little while too. Even if you remove all other sources of energy loss, such as friction, intuitively, I know it can't work the way he describes it, I just couldn't pick out what.
Then it dawned on me. The distance he needs to pull up the balls near to the center is farther than the distance to drop away from the center. It really needs diagrams to prove the point, but I'll try my best with words. Truly accurate math involve circular functions, which happen to be one of my weaker math fields. If I can figure this out without doing the necessary math, what's that to say about his intelligence?
To make the point as succinct as possible, take a pencil or ruler or some other appropriately long narrow object (a penis won't work) and figure out the physical center (not balanced center) and seesaw it back and forth around this center. Note the distance each end travels. as you seesaw the pencil.
Now move the "center point" to about three quarters of the way to either side. Now seesaw it back and forth around this center and note the distance each end moves.
That's the problem with his logic. If we assume a ratio of 2:1, at least two balls have to travel down the far side of the wheel in order to carry up one ball on the near side the required distance. (His ratio isn't exactly 2:1. It's probably more like 1.2:1.) This is exactly why two balls sometimes gets trapped in the same cup on the lifting side. Even if he figures out the exact number of cups on both the inner and outer part of the wheel and their exact positioning to
always ensure one ball per cup, he can't get away from the fact that it requires more balls going down to bring up
a ball the same distance. Eventually, he'll run out of balls.