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In this MSE question, this statement is proven:

Room is cube-shaped, with side 3m. 136 flies fly in it. Prove that at any moment one can encompass 6 flies with a sphere of radius 90cm.

Can the statement be strengthened in the sense that 6 is replaced with a larger number?

My intuition says that this is really possible.

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VividD
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  • This time I'd try to use a tight packing of the $136$ spheres (i.e. the coplanar centers form a hexagonal mesh) and prove that at least a certain number of spheres (I guess we can go up to the $12$ adjacent spheres, i.e. $13$ flies)... – AlexR Nov 07 '14 at 15:56

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