u/GDLingua_YT

Here is the exercise:

In a 30 student Math class they are playing the following game. The teacher rolls with 7 different colored D8s, and the students write the rolled numbers down in an arbatriary order, thus creating a 7 digit number. Just now the teacher rolled the following members: 1,2,3,4,5,6,7. Is it possible, that one student's number is a perfect multiple of another's?

Here's what I know:

1. The numbers the students write are, for our purposes, random, so if there exist at least one pair of such numbers, then the answer to the question is yes.

2. There are 7! = 5040 possible numbers, so a brute force search would be extremely unviable and time consuming

My problem: I can't think of any way (other than brute force) to check for these pairs, and I also have no way of proving the opposite.

So... , can y'all help me?