This is an old sorry, while giving a lecture on Functional Analysis, I suddenly changed the topic and asked this question::
I drawn this sequence on the board: 969,486,192,18,8. I asked my students about the origin of this sequence. Monica (name changed) instantly stuck up her hand. "Sir, in '969, 486, 192, 18, 8' each term is the product of the digits of the previous term. I continued, Now let me tell you about 969's persistence. The persistence of a number is the number of steps (4 in our example) before the
number collapses to a single digit. Now, consider 2 mighty difficult questions:
"1. What is the smallest number with persistence 3?"
"2. What is the smallest number with the persistence of 12? (Hint: This one is so difficult, don't even bother trying to solve it.)"