NOTE: Do not attempt this problem until you have finished all the other problems. Even if you do not attempt this problem you can still get an 80% (high enough for a first-class degree!) This problem is meant to reward those of you who have honed your algorithm / problem-solving skills and let those of you set yourselves apart.

The year is 3023. You are Dr. Susan Calvin, the world's leading robo-psychologist. You are in the room with three robots. One robot is always happy. The second robot is always sad. The third robot is happy half the time you ask him, and sad the other half. The robots used to be clearly labelled with a badge that said either "always happy", "always sad" or "half and half". However, your arch-nemesis Dr. Asimov, has stolen into your lab and switched the badges around so that every robot now is guaranteed to have an incorrect badge. 

You now need to switch the badges back to their correct robot. You can do this by asking each robot "how do you feel?" Design an algorithm that minimises the total number of times you need to ask the question "how do you feel?" What is the minimum number of times you need ask the question in order to solve the problem?