What is a minimal subset of unit cells in a cube of size N such that every orthogonally oriented column of cells contains at least one cell of the subset? Exactly one?
Inspired by extending the Salsa20 round function to higher dimensions. In 2D, a diagonal suffices.
One can also ask the continuous question: what is the surface with minimal area inside a cube which, when projected to each face, covers the entire face?
Hypercubes.
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