Weird thing is, in Google AI Studio all their models—from the state-of-the-art Gemini 2.5Pro, to the lightweight Gemma 2—gave a roughly correct answer. Most even recognised the packing efficiency of spheres.

But Google search gave me the exact same slop you mentioned. So whatever Search is using, they must be using their crappiest, cheapest model. It's nowhere near state of the art.