9.1. On a line, several points were marked. Then, between each pair of neighboring points, one more point was marked, and this operation was repeated once more. As a result, 101 points were obtained. How many points were marked initially?
9.1. Answer: 26. Solution. Let there initially be $k$ points marked. Then $k-1$ more points were added to them (one between the first and second, second and third, $\ldots, k-1$-th and $k$-th marked points), and then another $(k+(k-1))-1=$ $2 k-2$ points. In total, the number of points became $4 k-3$. Solving the equation $4 k-3=101$, we find the answer.