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A natural number $n$ is called sensible if there is an integer $r$ with $1<r<n-1$ such that the representation of $n$ in base $r$ has all the digits equal. For example, 62 and 15 are sensible, because 62 is written 222 in base 5 and 15 is 33 in base 4. Show that 1993 is not sensible, but 1994 is sensible.
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