8. (10 points) Select several numbers from $1, 2, 3, \cdots, 9, 10$ such that each of the 20 numbers $1, 2, 3, \cdots, 19, 20$ is equal to one of the selected numbers or the sum of two selected numbers (which can be the same). How many numbers at least need to be selected? $\qquad$
【Solution】The solution is as follows:
$$
\begin{array}{l}
1=1 ; 2=2 ; 3=1+2 ; 4=2+2 ; 5=5 ; 6=1+5 ; 7=2+5 ; 8=8 ; 9=9 ; 10=10 ; 11=1+10 ; \\
12=2+10 ; 13=5+8 ; 14=7+7 ; 15=5+10 ; 16=8+8 ; 17=8+9 ; 18=8+10 ; 19=9+10 ;
\end{array}
$$

By observation, it can be seen that selecting several numbers from $1, 2, 3, \cdots, 9, 10$ as $\{1,2,5,8,9,10\}$; can make each number in the 20 numbers $1, 2, 3, \cdots, 19, 20$ equal to a certain selected number or the sum of two selected numbers (which can be equal). Therefore, at least 6 numbers need to be selected. The answer is 6.