What is the smallest number that could be the date of the first Saturday after the second Monday following the second Thursday of a month?
1. Let's start by identifying the second Thursday of the month. If the month starts on a Thursday, the first Thursday is the 1st, and the second Thursday is the 8th.
2. Next, we need to find the second Monday following the second Thursday. Since the second Thursday is the 8th, the first Monday after the 8th is the 12th. Therefore, the second Monday is the 12th.
3. Now, we need to find the first Saturday after the second Monday. The second Monday is the 12th, and the first Saturday after the 12th is the 17th.

Thus, the smallest number that could be the date of the first Saturday after the second Monday following the second Thursday of a month is the 17th.

The final answer is $\boxed{17}$.