## Problem of the Day #377: Happy $n_b^\text{th}$ Birthday!March 30, 2012
Sreenath has foolishly forgotten how old Jon is. He knows Jon is $57$, $73$, or $91$, but can’t remember which. In an attempt to figure it out, Sreenath poses a clever math problem for Jon on his birthday (today). “Happy $n_b^{\text{th}}$ Birthday, Jon!” Sreenath says (where $b$, the base of $n$, is an integer greater than 2). Solve for $n$, given that it is three digits long.