2.1. Martha-the-needlewoman has many pins in her box. The first time she took out two pins, and each subsequent time she took out $k$ more pins than the previous time. It turned out that on the tenth time she took out more than 45 pins, and on the fifteenth - less than 90. Write down all possible $k$.
Answer: 5,6 (All answers)

Solution. The number of pins Marfa takes out on the $n$-th step is expressed by the linear function $2+k \cdot(n-1)$. Therefore, the inequalities $2+9 \cdot k>45$ and $2+14 \cdot k<90$ hold. From this, we have $\frac{43}{9}<k<\frac{44}{7}$, which gives the natural values $k=5$ and $k=6$.