17. (3 points) From the sixteen natural numbers $1,2,3,4, \cdots, 15,16$, if $n$ numbers are randomly selected, there must be two numbers such that one is three times the other. The smallest $n$ is $\qquad$.
【Solution】Solution: Group the numbers with a 3-fold relationship: $(1,3,9), (2,6), (4,12), (5,15)$, there are 4 groups in total,

the remaining 7 numbers each form a group,
thus, these 16 numbers can be divided into 11 groups. From the first group, you can take at most 2 numbers, i.e., 1 and 9, and from the other groups, you can take at most one number, meaning you can take up to 12 numbers to ensure that no number is three times another,

at this point, if you take one more, i.e., $12+1=13$ numbers, there will definitely be one number that is three times another. Therefore, the smallest $n$ is 13.