The first Google interview is most likely the easiest one.
I have the feeling that they normally ask general questions, just to ensure that you have some knowledge of computers and you are not just the guy who believes he deserves a place in Google because he can make nice Powerpoint presentations. At least happened in my case.
A guy from Mountain View called me sharply at the time we had arranged. He called on my mobile. I had everything arranged: From the bluetooth hands-free to nice and clean desk in front of me. At first, he asked me some questions about my CV, my age and my education. He didn't seem so interested in that and my impression was that his questions were somewhat mechanical.
After a couple of minutes, he started asking technical questions. The first one was easy: If we would like to index the entire earth population, how long should the index size be? Although a piece of cake, I felt like I was asked to prove that P=NP. Soon, I panicked but I asked for some time to 'warm up'. The Google Engineer was kind enough to understand and gave me all the time I needed in order to finally realize that I was talking to Google and that I had to control myself.
After recovering and answering to this question, I was put in front of a puzzle involving buckets and I was asked to find an algorithm that would end up in a situation that one bucket would be empty, as soon as some conditions were met. Excuse me for this vague description but I am still not able to remember exactly what the problem was all about. Instead of trying to find some exact solution to a problem that I couldn't understand (perhaps I was very nervous or I didn't understand the language), I followed an old Harry Truman's quote: "If you cannot convince them, confuse them". This seemed to work extremely well. I soon said something about modelling the problem as a Diophantine equation, where the solutions in integers would mean filling if positive or emptying if negative. Of course I had no idea what I was talking about, but the Google Engineer fell into it. He was not familiar with the idea, we soon started talking until we had switched to a more theoretical conversation. This gave me time to think over the solution and present with a backtracking-type of algorithm. During all this, I was asked some algorithmic-theoretical questions, for example about hashing space and time complexity.
We spent a lot of time on this problem. The last one was around his own domain of expertise. It turned out that this guy was working on Google Book Search and asked what I would if I had to find duplicates in book catalogs with entries with different titles but with the same content.. I had no idea of the format, Google was using to index book entries, I asked some questions that clarified the problem to me and then I presented my solution. My idea was to use some basic format properties of book text, for example number of paragraphs, size of paragraphs and so on. This way a book named "Albert Camus-The Stranger" would match a book "Famous Authors-L'etranger" (the example might not be realistic but it gives the idea)
The 45 minute had finished and it was time to ask my own questions. I asked a couple of things (one being if book search is still beta to which the engineer falsely responded that it is not!)and some other lame how-wonderful-is-Google questions and we said goodbye.
The next day I was informed by my recruiter that I had done well we had to proceed to the next stage. Overall, the guy I talked was very kind and showed a lot of understanding when I was stuck in the first and simplest question. But now I had to prepare for the 2nd interview which my recruiter had informed me that would be much more technical...
Continue to the second interview