How many positive whole numbers less than $100$ are divisible by $3$, but not by $2$?
1. **Identify numbers divisible by 3:**
   We need to find the positive whole numbers less than 100 that are divisible by 3. These numbers form an arithmetic sequence: \(3, 6, 9, \ldots, 99\).

   The general term of this sequence can be written as:
   \[
   a_n = 3n
   \]
   where \(a_n < 100\). To find the largest \(n\):
   \[
   3n < 100 \implies n < \frac{100}{3} \implies n < 33.33
   \]
   Since \(n\) must be an integer, the largest \(n\) is 33. Therefore, there are 33 numbers less than 100 that are divisible by 3.

2. **Identify numbers divisible by both 3 and 2 (i.e., divisible by 6):**
   We need to find the positive whole numbers less than 100 that are divisible by 6. These numbers also form an arithmetic sequence: \(6, 12, 18, \ldots, 96\).

   The general term of this sequence can be written as:
   \[
   a_n = 6n
   \]
   where \(a_n < 100\). To find the largest \(n\):
   \[
   6n < 100 \implies n < \frac{100}{6} \implies n < 16.67
   \]
   Since \(n\) must be an integer, the largest \(n\) is 16. Therefore, there are 16 numbers less than 100 that are divisible by both 3 and 6 (i.e., divisible by 6).

3. **Calculate numbers divisible by 3 but not by 2:**
   The numbers that are divisible by 3 but not by 2 are those that are divisible by 3 but not by 6. We subtract the count of numbers divisible by 6 from the count of numbers divisible by 3:
   \[
   33 - 16 = 17
   \]

Conclusion:
The number of positive whole numbers less than 100 that are divisible by 3 but not by 2 is \(\boxed{17}\).