Business Logic interview questions

I was walking around my college career fair when a guy in a company booth stopped me and said, "You know anything about software?" I said "yeah" and he gave me a short programming quiz on the spot. I aced the quiz and he set up an on-campus interview for me. He also mentioned that everybody who went for an interview was automatically entered into a random drawing for a big-screen TV. The on-campus interview was interesting. It wasn't the usual "tell me about yourself" interview. Instead, the interviewer had me solve algorithmic problems and brain teasers. One particular brain teaser was especially intriguing, and it went like this: “You have two strings and a lighter. Each string takes one hour to burn, but they burn at variable rates. So for example, after 30 minutes, you have no idea how much of the string has burnt. Using just the two strings and the lighter, determine when exactly 45 minutes have passed.” While I thought about the problem, the interviewer just sat there looking at me. After three intense minutes, I presented the correct solution, and he congratulated me. A few days later, the company called me up to schedule an on-site interview in Chicago. A few weeks later, I went to the company’s office in Chicago where I had three one-hour interviews with three different software developers. Each interview was highly technical, where I had to do things like draw out state machines on a whiteboard and write out test cases for hypothetical problems. During my on-site interview, I noticed that the company culture was very laid back. My interviewers wore jeans and T-shirts, and there was an Xbox in the office. I asked one of my interviewers if I could come to work everyday wearing sweatpants and no shoes. He said, “That’s perfectly fine, as long as you don’t mind walking around Chicago barefoot in the winter.”