Hint #1: Start by coming up with 4 requests spread out across the day that do not conflict, and then add a set of requests so that that your "target" requests each conflict with more than two other requests, and so there exists a request that only conflicts with two requests - both of them being part of your optimal solution. Make sure that once this conflict-two request is granted, and two more low- conflict requests are granted, that all of the others are in conflict with already-scheduled requests.