You were recently hired to be the head of maintenance in a mathematics building. The building has 61 doors but 60 our locked. In your office you have ten keys. Each key unlocks at least 1 door and no two keys unlock the same amount of doors nor the same door. There are ten rooms on a floor, with your office being in the basement (for technically an eleventh floor).
1. Develop an optimal strategy that will quickly tell you how many doors each key unlocks.
2. Develop an optimal strategy that will quickly tell you which door each key unlocks (if different from #1).