Let $b\geq 2$ be an integer. A real $r \in [0,1]$ is said to be *normal with respect to $b$* if every finite string made from the elements $\{0,\ldots,b-1\}$ appears in the $b$-ary expansion of $r$.

Are there integers $b, b'\geq 2$ as well as a real number $r\in[0,1]$ such that $r$ is normal with respect to $b$, but not with respect to $b'$?