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Let $\Gamma = \{0, 1, \sqcup\}$ be the tape alphabet for all TMs in this problem. Define the busy **beaver function** $BB: N \rightarrow N$ as follows. For each value of $k$, consider all $k-$state TMs that halt when started with a blank tape. Let $BB(k)$ be the maximum number of $1s$ that remain on the tape among all of these machines. Show that $BB$ is not a computable function.

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