To any triangle with side lengths $a,b,c$ and the corresponding angles $\alpha, \beta, \gamma$ (measured in radians), the 6-tuple $(a,b,c,\alpha, \beta, \gamma)$ is assigned. Find the minimum possible number $n$ of distinct terms in the 6-tuple assigned to a scalene triangle.

1. **Understanding the Problem:**
   We need to find the minimum number of distinct terms in the 6-tuple \((a, b, c, \alpha, \beta, \gamma)\) for a scalene triangle. A scalene triangle has all sides and angles distinct, i.e., \(a \neq b \neq c\) and \(\alpha \neq \beta \neq \gamma\).

2. **Analyzing the Relationship Between Sides and Angles:**
   For any triangle, the sides and angles are related by the Law of Sines:
   \[
   \frac{a}{\sin \alpha} = \frac{b}{\sin \beta} = \frac{c}{\sin \gamma}
   \]
   This implies that the function \(f(x) = \frac{x}{\sin x}\) is strictly increasing on \((0, \pi)\). Therefore, if \(a < b < c\), then \(\alpha < \beta < \gamma\).

3. **Considering the Number of Distinct Terms:**
   Since \(a, b, c\) are distinct and \(\alpha, \beta, \gamma\) are distinct, we start with 6 distinct terms. However, we need to check if any of these terms can be equal to reduce the number of distinct terms.

4. **Example of a Right-Angled Triangle:**
   Consider a right-angled triangle with sides \(a = \frac{\pi}{6}\), \(b = \frac{\pi \sqrt{3}}{6}\), and \(c = \frac{\pi}{3}\). The corresponding angles are \(\alpha = \frac{\pi}{6}\), \(\beta = \frac{\pi}{3}\), and \(\gamma = \frac{\pi}{2}\).

   - Here, \(a = \alpha = \frac{\pi}{6}\)
   - \(b = \beta = \frac{\pi}{3}\)
   - \(c\) and \(\gamma\) are distinct.

   Thus, we have 4 distinct terms: \(\frac{\pi}{6}\), \(\frac{\pi}{3}\), \(\frac{\pi \sqrt{3}}{6}\), and \(\frac{\pi}{2}\).

5. **Conclusion:**
   The minimum number of distinct terms in the 6-tuple \((a, b, c, \alpha, \beta, \gamma)\) for a scalene triangle is 4.

The final answer is \(\boxed{4}\).