8. Divide a circle into a group of $n$ equal parts and color each point either red or blue. Starting from any point, record the colors of $k(k \leqslant n)$ consecutive points in a counterclockwise direction, which is called a “$k$-order color sequence” of the circle. Two $k$-order color sequences are considered different if and only if the colors at corresponding positions are different in at least one place. If any two 3-order color sequences are different, then the maximum value of $n$ is . $\qquad$
8. 8 .

In a 3rd-order color sequence, since each point has two color choices, there are $2 \times 2 \times 2=8$ kinds of 3rd-order color sequences.
Given that $n$ points can form $n$ 3rd-order color sequences, we know $n \leqslant 8$.
Thus, $n=8$ can be achieved.
For example, determining the colors of eight points in a counterclockwise direction as “red, red, red, blue, blue, blue, red, blue” meets the conditions.