This is a delightful and very whimsical problem! However, it contains a fundamental misunderstanding of what "average distance" usually means in mathematics and geometry.

Let's break down why and how we might interpret it in a playful way:

**The Mathematical/Geometric Problem:**

*   **"Seven sleepy rectangles" and "one jealous teaspoon" are not well-defined geometric objects.** To compute a distance in geometry, we need precise definitions:
    *   **Rectangles:** We need their dimensions (length, width) and their positions (coordinates of at least one corner, and their orientation).
    *   **Teaspoon:** This is even more complex! A teaspoon has a 3D shape. We'd need a 3D model of it, its dimensions, and its position and orientation in space.
*   **"Average distance" between objects:**
    *   **Between two points:** This is straightforward (Euclidean distance formula).
    *   **Between a point and a line/plane:** Also well-defined.
    *   **Between two shapes:** This usually means the *minimum* distance between any two points on the respective shapes.
    *   **"Average distance" between *many* shapes:** This is highly ambiguous. Does it mean:
        *   The average of the minimum distances between the teaspoon and each rectangle?
        *   The average of the distances between their centers?
        *   The average of *all possible distances* between *every point* on the teaspoon and *every point* on all the rectangles combined? (This would involve complex integration and likely yield infinity if the objects have volume and aren't coincident).

**The Metaphorical/Poetic Interpretation (and how we solve it!):**

Since this isn't a solvable math problem in its current form, we switch to a more creative and interpretive approach.

*   **"Sleepy rectangles":** These suggest objects that are still, possibly lying flat, perhaps comfortable and unaware. Sleep implies a certain state of being.
*   **"Jealous teaspoon":** This is the key emotional element. Jealousy implies a desire to be *closer* or *like* the rectangles. It suggests a feeling of *distance* or *separation* that the teaspoon wants to overcome.

**Conclusion:**

Given the metaphorical nature:

The average distance between seven sleepy rectangles and one jealous teaspoon is **the distance of longing.**

The teaspoon wants to be among them, to be as comfortable or as settled as they are. Its jealousy creates an emotional chasm, which is the "distance" we're truly measuring here. It's not a physical measurement, but an emotional and relational one.

Therefore, the distance is **immeasurable by conventional means, but deeply felt.**
