We prove that the number of partitions of the hypercube ${\bf Z}_q^n$ into $q^m$ subcubes of dimension $n-m$ each for fixed $q$, $m$ and growing $n$ is asymptotically equal to $n^{(q^m-1)/(q-1)}$. For the proof, we introduce the operation of the bang of a star matrix and demonstrate that any star matrix, except for a fractal, is expandable under some bang, whereas a fractal remains to be a fractal under any bang.

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