6. Given 95 numbers $a_{1}, a_{2}, \cdots, a_{95}$, each of which can only take one of the two values +1 or -1. Then, the minimum positive value of the sum of their pairwise products $a_{1} a_{2}+a_{1} a_{3}+\cdots+a_{81} a_{23}$ is $\qquad$ .
6.13.

Let $N=a_{1} a_{2}+a_{1} a_{3}+\cdots+a_{98} a_{95}$.
Suppose $a_{1}, a_{2}, \cdots, a_{95}$ contain $m \uparrow+1, n \uparrow-1$, then $m+n=95$.
Multiplying (1) by 2 and adding $a_{1}^{2}+a_{2}^{2}+\cdots+a_{95}^{2}=95$, we get
$$
\left(a_{1}+a_{2}+\cdots+a_{95}\right)^{2}=2 N+95 \text{. }
$$

Also, $a_{1}+a_{2}+\cdots+a_{95}=m-n$,
$$
\therefore(m-n)^{2}=2 N+95 \text{. }
$$

The smallest natural number $N=13$, at this time,
$$
\begin{array}{l}
(m-n)^{2}=11^{2}, \text{ i.e., } \\
m-n= \pm 11 .
\end{array}
$$

Solving (2) and (3) simultaneously, we get $m=53, n=42$ or $m=42$, $n=53$. According to this, we can construct the case where $N$ reaches its minimum value.
Thus, the required minimum positive value is 13.

Solution 2: Suppose $a_{1}, a_{2}, \cdots, a_{95}$ contains +1 $n$ times, then -1 appears $95-n$ times. $S=a_{1} a_{2}+a_{1} a_{3}+\cdots+a_{94} a_{95}$ has $C_{n}^{2}+C_{95-n}^{2}$ terms of +1, and $C_{95}^{2}-\left(C_{n}^{2}+C_{95-n}^{2}\right)$ terms of -1.
$$
\begin{aligned}
S= & \left(C_{n}^{2}+C_{95-n}^{2}\right)-\left[C_{95}^{2}-\left(C_{n}^{2}+C_{95-n}^{2}\right)\right] \\
= & 2\left(C_{n}^{2}+C_{95-n}^{2}\right)-C_{95}^{2} \\
& =n(n-1)+(95-n)(94-n)-\frac{1}{2} \times 95 \times 94 \\
& =2 n^{2}-(95+94+1) n+\frac{1}{2} \times 95 \times 94 \\
& =2\left[\left(n-\frac{95}{2}\right)^{2}-\frac{95}{4}\right]>0 \\
& \Rightarrow\left|n-\frac{95}{2}\right|>\frac{\sqrt{95}}{2} .
\end{aligned}
$$

Thus, either $n>\frac{95}{2}+\frac{\sqrt{95}}{2}>47.5+4.8=52.3 \Rightarrow n \geqslant 53$ or $n<\frac{95}{2}-\frac{\sqrt{95}}{2}<47.5-4.8=42.7 \Rightarrow n \leqslant 42$.
(4.8 is an underestimate of $\frac{\sqrt{95}}{2}$),

When $n=53$, $S=2 \times 53^{2}-2 \times 95 \times 53+\frac{1}{2} \times 95 \times 94=13$. Similarly, when $n=42$, $S=13$.
From the function graph, the minimum positive value of $S$ is 13.