This seems like something a 5 minute FizzBuzz-esque programming assignment as a pre-filter could easily fix. The goal seems to be a barrier that only serious applicants will even bother to attempt, and that's fair. But when that barrier then becomes a 4+ hour time sink for the serious applicants it becomes a problem. There are plenty of hackerrank style sites where someone can show a bare minimum of competency without costing either side much time.
yeah I think 4 hours is a bit too much, in the end you only need competency as a screening.
we used to give out this http://play.elevatorsaga.com/#challenge=3 and asking for solution to level 3 which can be done in a short time + is the first non trivial challenge.
of course solutions can be find in internet etc, but it's pretty easy to look them up if they smell fishy and it'd all come down crashing at the face-to-face anyway
it's also a very good exercise in real world problem solving and a source of endless technical discussion since there's no single good approach, especially with two elevators to schedule.