What's the Big Idea?

We had to do some brainstorming for one of our courses today. It was a good exercise because it's not that often that you get a group of smart people together and devote 1.5 hours solely to brainstorming startup ideas. No idea was too small or weird to discuss, so we went through everything from improving nail salons to bike ordering to online dating to social networks to men's socks.

I usually think of 2 ways to find startup ideas: thinking of problems and how to solve them, and thinking of great business models and how to apply them in new ways. In the first you find problems in your life or the lives of others and think of ways to solve them (say, it's annoying to buy socks all the time, why not subscription socks?), and in the second you apply great business models in new ways (birchbox is a great model, what about a birchbox for kids' toys?)

What I'd be interested to know is, where do entrepreneurs usually come up with ideas typically? Is it through methodically thinking through problems and how to solve them? Is it taking inspiration for great ideas and applying them elsewhere? Is there a process to coming up with great startup ideas, or is it usually more pure inspiration and luck?