# 1. CONDITION 

On a line, several points were marked. Then, between each pair of adjacent 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?
Solution. Let there be $k$ points marked initially. 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 $(k+(k-1))-1=2k-2$ points. In total, the number of points became $4k-3$. Solving the equation $4k-3=101$, we find the answer.

Answer: 26.