Palantir Technologies interview questions

I had 2 unofficial 60+ minute conversations with current employees who encouraged me to apply for this position and then referred me internally. After submitting my application, I had a response from HR by the end of the day. HR scheduled a never ending series of phone calls. My first was with HR and I was asked some questions related to math and computer science. "I'm thinking of a number between 1 and 1000, how would you guess it and on average how many guesses would you need? (binary search)." "You invest equally in two stocks. Over the next 100 days the flucuate up and down every day by $1 or $10. After 100 days which stock has the highest value?" Next came 3 phone calls with actual product experts. I really enjoyed these conversations and they all ran over the allotted time. I was asked how I would solve some nebulous problems "a grocery store wants to know what music to play to increase sales, how would you solve this problem?" I felt that they were most interested in hearing me think and I took it as an opportunity to work with what might become my colleagues. I thought we came up with some plausible and imaginative scenarios, and every one on the phone was very encouraging - "I hope we'll get a beer soon.". After my third call they flew me out for an onsite and the demeanor was markedly different. The interviews were supposed to start at 9 but got pushed back to 10:30 and the entire office seemed too busy to care I was there. At one point I sat alone in a room for 25 minutes and there was no lunch. I was asked to white board code some stats problems, split a sequence of numbers into all subsets, etc. My final interviewer asked me "to list some times I exhibited exemplary leadership." The question was clearly a snide to the fact I was just finishing my PhD and had no "real-world" experience and I found it a silly question to ask after I had been going through their rigorous process for nearly 2 months and was flown out and put up on their dime. A week later I received a rejection letter. I should have boozed and dined on their dime after the day was over. The company does seem like a great place to work but I'm convinced that most of the job would involve cleaning data and giving companies the ability to off large swaths of their analysts. Where's the challenge?

Initial screen by telephone. Had to use Palantir software from home and answer some questions. Final interview at office. 2 one-on-ones and 1 two-on-one. Behavioral questions, cases, and asked to consider how Palantir could approach healthcare.