4. Julian wants to make a list of numbers as long as possible. Each number on the list must consist of one or more of the digits 1 through 9. Additionally, it must be true that

- each of the digits 1 through 9 is used exactly once;
- no number on the list is divisible by any other number on the list.

What is the maximum number of numbers that Julian's list can contain?
A) 4
B) 5
C) 6
D) 7
E) 8
A4. D) 7 The only list of 9 numbers that meets the first requirement consists of the nine digits each as a separate number. This list does not meet the second property (since 2, for example, is divisible by 1).

A list of 8 numbers that meets the first requirement must consist of seven single-digit numbers and one two-digit number. According to the second property, however, no more than five digits can appear individually: in addition to the digits 5, 7, 9, at most one of the digits $1, 2, 4, 8$ and at most one of the digits 3, 6 can appear individually.

A list of 7 numbers that meets the requirements does exist, for example: 5, 6, 7, 8, 9, 23, 41. The maximum length of Julian's list is therefore 7.