Google typically didn't ask fermi problems like that. Although, actually, sphere packing problems are pretty interesting, mathematically...

A common classic era Google question would be roughly "find an O(n) or O(logn) solution to a problem that most people would solve quadratically, and write pseudocode for your solution, handling important edge cases, while also intuiting the special details that your interviewer is fishing for (because they learned it in their PhD)".

So many people I knew at google were great math and science folks who ended up writing CRUD apps. Really depressing for them.