3. There are 49 children, each with a number on their chest, ranging from 1 to 49, all different. Please select some of the children and arrange them in a circle so that the product of the numbers of any two adjacent children is less than 100. What is the maximum number of children you can select?
3. Since the product of any two different two-digit numbers is always greater than 100, according to the conditions of the problem, two two-digit numbers are not allowed to be adjacent. This means that a one-digit number should be inserted between two two-digit numbers.
The problem asks for the maximum number of children that can be selected, so a two-digit number should be inserted between two one-digit numbers.
Now arrange the nine one-digit numbers $1-9$ in a circle, which creates 9 intervals where two-digit numbers can be inserted.
Therefore, the maximum number of children that can be selected cannot exceed 18.