A wooden cube, whose edges are one centimeter long, rests on a horizontal surface.  Illuminated by a point source of light that is $x$ centimeters directly above an upper vertex, the cube casts a shadow on the horizontal surface.  The area of the shadow, which does not inclued the area beneath the cube is 48 square centimeters.  Find the greatest integer that does not exceed $1000x.$
1. **Understanding the Problem:**
   - A wooden cube with edge length 1 cm is placed on a horizontal surface.
   - A point source of light is positioned \( x \) cm directly above an upper vertex of the cube.
   - The shadow cast by the cube on the horizontal surface, excluding the area directly beneath the cube, is 48 square centimeters.

2. **Calculating the Total Shadow Area:**
   - The shadow includes the area directly beneath the cube (1 cm\(^2\)) and the additional shadow area (48 cm\(^2\)).
   - Therefore, the total shadow area is \( 48 + 1 = 49 \) cm\(^2\).

3. **Determining the Ratio of Similitude:**
   - The shadow forms a square with an area of 49 cm\(^2\).
   - Since the area of the shadow is 49 cm\(^2\), the side length of the shadow square is \( \sqrt{49} = 7 \) cm.
   - The ratio of similitude (scaling factor) between the shadow and the cube is \( 7 \), because the side length of the cube is 1 cm.

4. **Relating the Distance from the Light Source:**
   - Let \( h \) be the height of the light source above the horizontal surface.
   - The distance from the light source to the upper vertex of the cube is \( x \) cm.
   - The distance from the light source to the lower vertex of the cube is \( x + 1 \) cm.
   - The ratio of the distances from the light source to the upper and lower vertices of the cube is \( \frac{1}{7} \).

5. **Setting Up the Proportion:**
   \[
   \frac{x}{x + 1} = \frac{1}{7}
   \]

6. **Solving for \( x \):**
   \[
   7x = x + 1
   \]
   \[
   7x - x = 1
   \]
   \[
   6x = 1
   \]
   \[
   x = \frac{1}{6}
   \]

7. **Finding the Greatest Integer Not Exceeding \( 1000x \):**
   \[
   1000x = 1000 \times \frac{1}{6} = \frac{1000}{6} \approx 166.6667
   \]
   - The greatest integer that does not exceed \( 166.6667 \) is 166.

The final answer is \( \boxed{166} \)