"However, the numbers follow a grid, with rules nobody told me."

I learned it from reading a state map about forty years ago. The legend succinctly explained the system. Without digging through a pile of paper maps, that might still be the case. Regardless, these rules are probably clearly documented from a simple web search, despite that no one has felt the need to "tell" the author what the rules are.

EDIT: "interstate numbering system" on DDG brings up the Wikipedia page as the first link, and that link explains it. There's no mystery here, though my query string does assume that one assumes a "system" to be explained.

And while I'm editing, state routes and U. S. Routes kind of follow the same pattern, especially the N/S and E/W designations. Would have to go search to verify other commonalities.