The complete problem is the following:

> You have a set of numbers of the form M = { 7, 77, 777, …, 77…7
> (n times) }.
> 
> Can it be that you have two disjoint sets A and B such as $A \cup B = M$
> have the property that the product of A's elements equals the product
> of B's elements?

Note: it's from a collection of problems for the 6th grade but I don’t mind of any solution.