Recreational mathematics

I've become a sucker for evening logic puzzles. It makes me the victim of disdain in social drinking situations, impatiently waiting for me to join in the conversation and put the notebook away, until math-tutor-David imposes said problems on the whole table.

The starting problem:

Three applicants for a job are all equally qualified. In order to distinguish between them, the employer presents them with a fair test. Each applicant is blind folded and seated facing one another in a triangular shape. The employer has three black hats and one white hat. He places one hat on each of the applicants and toss the other one out. When the blindfolds are removed the first one to state his or her hat colour will get the job.

Before the blindfolds are removed, one applicant states that he knows his hat colour and he knows why. What is it and why?

[I think this problem would have been a lot easier if I'd seen it written down rather than verbally...it's easy to forget information when there's beer involved...]

The current problem:

There are seven prisoners, each to be executed tomorrow. The warden presents them with a chance to save their lives. Before the execution each prisoner will be chosen at random to enter a room. In the room will be two light switches. The light switches serve no purpose. The prisoner must flick one switch once. When a prisoner can tell the warden when he knows all seven prisoners have flicked a switch, they may all live. They have one evening to discuss the problem. What should they do?

Since I'm that kind of fair-play kind of player, I haven't looked any answers up online. Of course now I've written them online, I'm potentially subject to spoilers. Just stay smug in the knowledge you know something I don't (yet), ok? :P