Here’s a problem inspired by Luyi’s “Satiated Clam” problem. (Her problem makes me think of a clam with the biggest possible pearl inside.) The problem begins with the same setup as hers.

Let *ABCDEF* and *ABC’D’E’F’* be two regular hexagons with unit side length. Suppose that their dihedral angle is . Let P be the convex hull of the two hexagons. For which is the volume of *P* maximal and what is this maximal volume?

I guess this one can be called the “Greedy Clam” problem, perhaps.

(Here’s a solution.)

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Love the name! When I was coming up with this problem, I originally named it the “USAMTS Clam.” Glad that others sense similar nomenclature, too 🙂

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