I will try to get from that to a 6th grade level - fingers crossed - I'm starting to dust off my math.

@MarcoRipà I've reached the conclusion that numbers like 777777 having 6k digis have (at least) an additional 7 when being decomposed, but I still haven't managed to do anything about it. That's why I was initially asking how to prove that the product of all numbers from set M cannot be a perfect square - my intuition tells me that P(A) cannot be equal to P(B) where P represents the product of A/B elements.