To compute the average distance between seven sleepy rectangles and one jealous teaspoon, we must first define the parameters of this non-Euclidean domestic crisis.

### 1. Variables and Geometry
*   **The Rectangles ($R_1$ through $R_7$):** Being "sleepy," these rectangles exist in a state of low-energy repose. We model their centers as points on a 2D kitchen plane. Let us assume they are distributed in a lazy circle around the center of the kitchen table with radius $r = 10$ cm.
*   **The Teaspoon ($T$):** The teaspoon is "jealous," meaning it is actively avoiding the rectangles to maintain its personal space. We place the teaspoon at the origin $(0,0)$ relative to the table, but displaced by the "jealousy constant" ($\delta$), effectively pushing it to the edge of the silverware drawer at coordinate $(15, 15)$.

### 2. The Distance Formula
The distance $d_i$ between the teaspoon $(x_T, y_T)$ and any rectangle $R_i$ positioned at $(x_i, y_i)$ is given by the Pythagorean theorem:
$$d_i = \sqrt{(x_i - x_T)^2 + (y_i - y_T)^2}$$

For a set of $n=7$ rectangles arranged in a circle of radius $r=10$ around the origin, the coordinates are $(10\cos\theta_i, 10\sin\theta_i)$. With the teaspoon at $(15, 15)$, the distance to the $i^{th}$ rectangle is:
$$d_i = \sqrt{(10\cos\theta_i - 15)^2 + (10\sin\theta_i - 15)^2}$$

### 3. Computation
Expanding the terms:
$$d_i = \sqrt{100\cos^2\theta_i - 300\cos\theta_i + 225 + 100\sin^2\theta_i - 300\sin\theta_i + 225}$$
Using the identity $\sin^2\theta + \cos^2\theta = 1$:
$$d_i = \sqrt{550 - 300(\cos\theta_i + \sin\theta_i)}$$

To find the average distance ($\bar{d}$), we integrate over the distribution of the seven sleepy rectangles:
$$\bar{d} = \frac{1}{7} \sum_{i=1}^{7} \sqrt{550 - 300(\cos\theta_i + \sin\theta_i)}$$

Assuming the rectangles are spaced at intervals of $2\pi/7$, we calculate the average displacement from the origin. Numerically, the value of $\sqrt{550 - 300(\cos\theta + \sin\theta)}$ averaged over a full rotation is approximately **23.1 cm**.

### The Final Result
Given the inherent instability of sleepy geometry and the emotional volatility of silverware, the average distance is:

**$\approx 23.1$ centimeters.**

*Note: If the teaspoon becomes significantly more jealous, the distance will increase proportionally to the depth of the silverware drawer. If the rectangles fall fully asleep and cease to be geometric entities, the distance becomes undefined.*
