Let Qn be the n-dimensional Hamming cube and N = 2n. We prove that the number of maximal independent sets in Qn is asymptotically 2n2N/4,\documentclass[12pt]{minimal}
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\begin{document}$$2n{2^{N/4}},$$\end{document} as was conjectured by Ilinca and the first author in connection with a question of Duffus, Frankl and Rödl.