99 dwarfs stand in a circle, some of them wear hats. There are no adjacent dwarfs in hats and no dwarfs in hats with exactly 48 dwarfs standing between them. What is the maximal possible number of dwarfs in hats?
1. **Numerate the dwarfs**: Label the dwarfs as \( A_1, A_2, \dots, A_{99} \).

2. **Rearrange the order of dwarfs**: We need to rearrange the dwarfs in a way that satisfies the given conditions. Consider the sequence:
   \[
   A_1, A_{50}, A_{99}, A_{49}, A_{98}, \dots, A_2, A_{51}
   \]
   This sequence ensures that no two adjacent dwarfs in the sequence are adjacent in the original circle, and no two dwarfs in the sequence are exactly 48 positions apart in the original circle.

3. **Determine the maximum number of dwarfs in hats**: We need to ensure that no two adjacent dwarfs in the sequence wear hats. To maximize the number of dwarfs in hats, we can place a hat on every third dwarf in the sequence. This ensures that no two adjacent dwarfs in the sequence wear hats.

4. **Calculate the maximum number of dwarfs in hats**: Since there are 99 dwarfs, and we place a hat on every third dwarf, the maximum number of dwarfs in hats is:
   \[
   \left\lfloor \frac{99}{3} \right\rfloor = 33
   \]

5. **Verify the conditions**: 
   - No two adjacent dwarfs in the sequence wear hats: By placing a hat on every third dwarf, we ensure that no two adjacent dwarfs in the sequence wear hats.
   - No two dwarfs in hats are exactly 48 positions apart in the original circle: The rearrangement of the sequence ensures that no two dwarfs in hats are exactly 48 positions apart in the original circle.

Therefore, the maximal possible number of dwarfs in hats is 33.

The final answer is \(\boxed{33}\)