Wow, I just went through the exact same thing (except it took 5 months!). I had 5 interviews (1 non-technical) which went really well, then a sixth, and final, technical interview with the VP of Engineering in which he threw at me a math puzzle that I had never seen before. Of course it's in pseudocode in a Google Doc, so it's basically sink or swim.

I did OK, but only OK on it. His comment when we ran short of time was "Yeah, I think with a little debugging, that solution would probably work" but then he passed.

Perhaps it's just my bruised ego, but I think he made a bad decision. Here he is with 5 members of his own team saying that I'd be a great fit, but he basically selects for people who have encountered a puzzle with very little relation to the actual work involved in the role. He may as well have evaluated me as a developer on my ability to prepare a chocolate souffle in 30 minutes. It would have been roughly as representative of my skill set.

Every detail you just described exactly mirrors my experience. The VP of engineering, the math puzzle I hadn't seen before, trying to solve it in a Google doc rather than with code I could compile. All of it.

I did end up solving it, but I wasn't happy with the solution and neither was he, with good reason of course, but it was one of those problems I easily could have solved if given the proper time to work on it rather than digitally whiteboarding it for 20 minutes in a high pressure situation. A quick and dirty solution is all you should expect from working on a never before seen problem in 20 minutes on paper without a compiler.

I came away feeling as though their process was more broken than my performance. Doubtless, I could have done better. But it just felt so strange to be washed out after four other engineers thought I was qualified.

The high pressure situation makes things hard. In a recent interview, I turned

   P(A and B and C) = P(A) + P(B|A) + P(C|AB)

rather than the product of the probabilities just because I was stressed, then got a nonsensical answer. Fortunately the interviewer just asked me to reconsider that line, but it was not a mistake I would normally make.

An aside, but do they really normally run a 2-month interview process, or was it some kind of scheduling issue? Seems like a lot of candidates wouldn't even stick around for the end of that, since they'll have gotten an offer from somewhere else before then.

Probably a combination of scheduling issue + normal process. I got the impression they subject candidates to much more vetting than normal, but it was also not uncommon for a week or more to go by between interviews.

I will ask the same questions to different interviewers. Often, I will get different answers/perspectives on things.

I'll sometimes even say, "I've asked some of these questions to [person x, person y, ...], but I'd like your perspective."

That's what I had to resort to. But I felt that the fact that I wasn't fielding an original, unasked question was somehow counting against me.

Wow, next time at my first interview if they ask if i have any questions i'll ask how many more interviews i'll have to do...

I usually ask "Where do we go from here?" or "What does the process look like from here on?" or some such.

Interesting responses here. Maybe I could suggest to do a little more research on the company's standing (I really don't know myself). A lot of times when companies are seeking to sell, they start interviewing folks to create a perception to potential investors the company itself is doing well. In reality perhaps they can't afford to hire and are simply trying to sell the company off. There could be any number of reasons outside of the interview itself that you are unaware of. E.g - Another candidate (which doesn't sound like the case here). Don't beat yourself up to much over it. It sucks that due to stupid legalities, we can't get the full details for why we were rejected. Perhaps the issue we really need to fix here is creating a better more transparent interview process.

Also to the person whose interview took 5 months. Is this really a company you would want to work for? Sounds like they don't have their shit together.

when i was interviewing at olark, I also had about four interviews and at the third i declined the "do you have any questions?"

but i didn't just say no, i explained that i already had two other interviews and the other interviewers had answered all my questions.

i got hired, so i'm not sure if that's related or not.

Yeah, that's what I told the interviewer as well.