【Question 25】
From 49 balls labeled with numbers 1 to 49, select several balls and arrange them in a circle so that the product of the numbers on any two adjacent balls is less than 100. How many balls can be selected at most?
【Analysis and Solution】
The problem of extremum.
$$
9 \times 10=90,10 \times 11=110 \text { ; }
$$

Therefore, any two balls with numbers not less than 10 cannot be adjacent; that is, at least one of the adjacent two balls must have a number less than 10; hence, the maximum number of balls that can be selected is $9 \times 2=18$. For example, as shown in the figure below.