It's a nice puzzle, but the solution wasn't as generalized as I'd have liked. Isn't there a way to do it with calculus, even if it requires differential equations using max points and tied elements? And while it's nice to use intuition for the multiples of 1000, intuition isn't rigorous even if correct
For the record, when I approached it I only thought of equal distance drop points (it's practical when there is no underlying plan for the time being, to use trial and error with neat cuts), and so ended with the suboptimal 500 bananas (instead of the possible 533), by dropping (eg) 500 bananas at the 1/4 point, then dropping 250 bananas at the 2/4 point (and using 250 from the 1/4 point on your way back), then finishing the trip with using the 500 in the two points, thus ending with 500. But it wasn't generalized, just one case, obviously there could be others and it could always be suboptimal (as it was).
