Google Produktmanager interview questions

A recruiter reached out through LinkedIn. Was easy to work with and helped set me up with a phone screen. Phone screen was a short product design question about how I would design an app for my favorite sports team (I had the choice between this and another question not related to sports). After passing the phone screen got passed to a new recruiter who helps with the rest of the process. Was brought on site for a day of being interviewed by 4 different PMs and 1 SWE. Mostly standard PM questions around product design and metrics. SWE had two parts: implementing a fibonacci algorithm, first naively and them optimizing (iterative vs. recursive, memoizing, etc...) and the a systems design question around implementing Google Instant. I thought the interviews went well, but the still couldn't decide so they brought me in again for a second round of onsites. This time I only met with senior two people, a high-level SWE (had been at Google for 9 years) and a Director of PM. These went well and my final package was approved by the hiring committee about two weeks after the second round. Throughout the interviews there were no brainteasers or estimation questions. The closest thing was the ladder question I included below, which is really more of a CS/algorithms question. Overall the process took much longer than expected, about 3 months from initial contact to offer. Google feels big and it is big. I also interviewed at Twitter and Facebook and the size differences jump up an order of magnitude for each step (Twitter -> FB -> Google). It also noticeably feels like an older company, i.e. interviewing with people who have been at Google since before FB or Twitter were founded. This isn't a bad thing, just an observation.