uncompetence

Small nit: Watson, not Deep Blue.

Except that's not how public safety works. Part of why this regulation exists is because having unregulated taxi drivers (at least to the judgement of lawmakers) poses a danger to everyone else on roads etc.

"For example, infants don't have spacial awareness, or understand how objects can be relative to each other, until they learn the words for describing relativity."

Where's the citation on this?

Why the hell is recursion considered cheating?

If you treated this as a variant on the backpack problem, you run into trouble as you can't properly memoize or use dynamic programming. You use 'timesteps' as the size of the 'knapsack' since the number of balls is unbounded. At each timestep, you cannot determine the the optimal solution to the subproblem and you'd have to save every possible ball combination.

TL;DR - It gets to be a pretty messy/bad backpack and should probably be solved another way

If it is any consolation, I'm pretty sure Mr. Thompson is a 14 year old kid.