Two mirror walls are placed to form an angle of measure $\alpha$. There is a candle inside the angle. How many reflections of the candle can an observer see?
To determine the number of reflections of a candle that an observer can see when two mirror walls form an angle of measure \(\alpha\), we can use the concept of image formation by multiple reflections. Here is a step-by-step solution:

1. **Understanding the Geometry of Reflections:**
   When two mirrors form an angle \(\alpha\), the reflections of an object placed between them can be visualized by considering the repeated reflections of the object in each mirror. Each reflection in one mirror can be reflected again in the other mirror, creating multiple images.

2. **Using the Concept of Symmetry:**
   To simplify the problem, we can imagine extending the mirrors to form a complete circle by repeating the angle \(\alpha\) around a point. This would create a full circle of \(360^\circ\).

3. **Calculating the Number of Reflections:**
   The number of times the angle \(\alpha\) fits into \(360^\circ\) gives us the number of sectors formed by the mirrors. Mathematically, this is given by:
   \[
   \frac{360^\circ}{\alpha}
   \]
   Since we are interested in the number of reflections, we need to consider the greatest integer function (floor function) to count the complete sectors:
   \[
   \left\lfloor \frac{360^\circ}{\alpha} \right\rfloor
   \]
   This represents the number of distinct images formed by the reflections.

4. **Subtracting the Original Candle:**
   The observer sees the original candle plus the reflections. Therefore, the number of reflections seen is:
   \[
   \left\lfloor \frac{360^\circ}{\alpha} \right\rfloor - 1
   \]

5. **Conclusion:**
   The number of reflections of the candle that an observer can see is given by:
   \[
   \left\lfloor \frac{360^\circ}{\alpha} \right\rfloor - 1
   \]

The final answer is \( \boxed{ \left\lfloor \frac{360^\circ}{\alpha} \right\rfloor - 1 } \).