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**Number of "independent" subcubes of a hypercube**

Hello, I am trying to solve this problem: I have an

**n**-dimensional hypercube and

**m**of its vertices. Now I want to compute the maximum number of subcubes of the entire hypercube such that:

- each subcube from the set may contain only those

**m**vertices

- no subcube from the set is part of another subcube from the set

Does anybody have any idea?

Thank you very much.

Best regards,

Standa