1. The path from school to home is 140 m. Kolya covered this distance in 200 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: $a \in\left[70 ; \frac{14000}{199}\right)$.