8. The sum of several consecutive natural numbers, 
starting from one, is a two-digit number, both digits of which are the same. How many numbers were taken?
8. According to the condition of the problem, we form the equation $1+2+3+\ldots+n=10 a+a$, from which $\frac{n(n+1)}{2}=11 a, n^{2}+n=22 a, n=\frac{-1+\sqrt{1+88 a}}{2}$.

$1 \leqslant a \leqslant 9, a$-integer. By trial, we establish that the problem is possible for $a=5, n=10$ and $a=6, n=11$.