1. (10 points) Among 2017 natural numbers, there is at least one two-digit number, and among any two numbers, there is at least one three-digit number, then there are $\qquad$ three-digit numbers in these 2017 numbers.
【Analysis】According to the problem, among the 2017 natural numbers, there is at least one two-digit number, and among any two numbers, there is at least one three-digit number. Therefore, the number of two-digit numbers cannot be greater than 2. If there are 2 or more two-digit numbers, then it is possible to pick two that are both two-digit numbers, which contradicts the problem statement. Hence, there can only be 1 two-digit number. It is not difficult to find the number of three-digit numbers.

【Solution】According to the analysis, among the 2017 natural numbers, there is at least one two-digit number, and among any two numbers, there is at least one three-digit number,

then the number of two-digit numbers cannot be greater than 2. If there are 2 or more two-digit numbers, then it is possible to pick two that are both two-digit numbers, which contradicts the problem statement. Hence, there can only be 1 two-digit number, and the number of three-digit numbers is: $2017-1=2016$.

Therefore, the answer is: 2016.