1. The path from school to home is 180 meters, and Kostya covered it in 300 steps, with the length of each step being no more than $a$ cm, and the sum of the lengths of any two steps being greater than the length of any other step. What values can the number $a$ take under these conditions?
Answer: $a \in\left[60 ; \frac{18000}{299}\right)$.