Estimation quiz!

[EdS2]

Excellent - so 23 is a solid answer, and Valentin's estimate of 23 is spot-on. Valentin, that's a very good estimate indeed, and I'd love to know how you approached it.

As for the likelihood of performing this feat with real Moons, well, yes, as the Moon has enough matter to pull itself into something of a spherical shape, then an assemblage of several is doomed to become solidly spherical in due course. However, as the old joke has it "consider a spherical cow." Or in this case, some scale models of the Moon in the form of marbles.

Nice links found - thanks for sharing - but this quote
> The classical sphere packing problem, still unsolved even today
has become out of date. Kepler's conjecture has been proved, some ten years after this book, and then formally proven some 16 years later.

It's interesting, I think, that a random packing of spheres (or marbles) will have a density around 65%, the closest packing achieves a density of 74%, but the constraint of fitting into a sphere reduces us to about 47%. That's comparable to this surprising result: "The strictly jammed sphere packing with the lowest density is a diluted fcc crystal with a density of only 0.49365"