Frankly, it's just a pattern I've observed from playing with numbers myself. I'm unsure how to explain it properly, and I have no academic sources to point towa

Frankly, it's just a pattern I've observed from playing with numbers myself. I'm unsure how to explain it properly, and I have no academic sources to point toward. You can probably find a better explanation somewhere in an article on optimization problems. The intuition is that (e) is the optimal water-level when limited water is distributed among a variable amount of buckets where all the filled buckets multiply each other. Alternatively, it's like how volume() is maximized where volume(x, y, z) = (x y z) const = (x + y + z) when (x = y = z). Except in our original situation, the number of dimensions is arbitrary instead of fixed.