Question 14
Let $b \ge 2$ be an integer. Call a positive integer $n$ *$b$-eautiful* if it has exactly two digits when expressed in base $b$ and these two digits sum to $\sqrt{n}.$ For example, $81$ is $13$-eautiful because $81 = \underline{6}\,\underline{3}_{13}$ and $6 + 3 = \sqrt{81}.$ Find the least integer $b \ge 2$ for which there are more than ten $b$-eautiful integers.