Amazon Software Development Engineer, interview questions

I had a phone interview with Amazon. I was referred by a friend from mitbbs, and was contacted by a recruiter about one week after the referral. We set up a time for the first phone interview. The recruiter was responsive and nice, and the only weird thing was that she mentioned she would send me some application forms but she never did. I didn't quite have a real expectation to get an offer from Amazon. For the first phone interview, I was surprised that the interviewer called 3hours earlier than I expected, but it turned out to be my mistake :( I didn't pat attention to the time zone. Even though I was caught by a surprise, the first phone interview was just a piece of a cake for me, the coding problem was simply deleting some numbers in an array. After that there was an even simpler classic problem: in an array, all numbers appear twice except one special number, how to find that number. I told the interviewer with honesty that I knew the problem and he moved on to the next. The next and also last problem was asking, if you have two eggs, N floors, how to find the critical floor number below which all eggs dropped will not break, and above which all eggs dropped will break. By the way, their interviewers are really really nice. I was informed about passing the first interview only two days later. I had the second interview about two weeks later during travel. I was not fully prepared but I was much less nervous than the first time, as I was getting very close to my dream offer from another company. The interviewer called, and started with asking me why I want to be a software engineer. Then he asked me about some knowledge and concepts of hashing, which I was quite familiar with. After that was the coding question, which was sent to me as an email. After reading the problem and explaining my approach to the interviewer, he decided not to have me write the code! I still couldn't figure out why, since clearly the title of the email said "coding question". Maybe I left him an impression that my coding skills were so strong that he didn't even need to see it? But I never demonstrated any of my coding skills to him. The last problem was OOD, as expected from Amazon's interview. I was relatively weak in this area, but I managed to grab some key words and key ideas which made him somewhat content. I was notified about the result a couple of days later, and I was told by the recruiter that I did very well in my phone interviews, although I personally doubt it...