Disappointed by solution

Warning, I reveal a safe code in this post.

While watching someone else play (a dangerous game to play when I'm not done myself), they solved the safe in >!the drawing room.!<

I had been struggling for a long time to figure that one out. I knew there had to be a connection between >!small gates and small gaits!<, but none of the solutions I tried worked. Even tried brute forcing for a little bit.

And then the person I'm watching just says, >!"Hmm, what if we separate the men and the women? So... 4 women. And... 15 men. So 4/15?" Tries 0415. It works.!<

I don't think I would have EVER thought of this. Was this intuitive to other people? Is there some other clue in the game suggesting to >!separate men and women at some point!<? If there is, you can just say "yes." Don't explain to me where.

Or is this the type of thinking I should be using to solve other puzzles throughout the game?