I just got back from the DC interview, where I was accepted for subs. I'll tell most of my experience the day of the interviews. It was held from May 17-19, but the actual interviews took place on the 19th.
At around 0630, we met up at the Starbucks and walked to the building. Naval Reactors I guess. The first round of interviews started around 0815. Pretty much everyone went at the same time, and the questions you got depended on which engineer you were assigned to. The consensus was that if you were an EE, you were going to get advanced circuits questions. Anyway, my first interview I got 3 questions. I feel I only got 3 because I took so long on the last question, that he didn't have time to ask anymore. Here are the questions.
1. You are standing on one side of a river that has no current. The river width is 3 miles, and you need to get to a point on the other side, and downstream 8 miles. You can swim at a rate of 3 mph, and run at a rate of 6 mph (I don't remember the exact rates). What is the path you should take to minimize the time to get from start to finish? When I have my final answer, he also told me to tell him the total time, as well as justify my answer.
2. Take the function y=1/x, from 1 to infinity and rotate it around the x axis. What is the volume you get? Also, what is the area under the curve using the same limits. He also asked me to explain why the volume was finite, but the area was infinite.
3. Kinda hard to explain this one. But it was a basic circuit that had two voltage sources, then one resistor, and then 2 resistors in parallel. He asked me to find the power going through a specific resistor. This is the problem I got stuck on. Just like everyone else has said, don't give up and explain what you are trying to do. So many times I just wanted to say "next question". But I found a mistake in my algebra and found out how to do it. I wasn't able to write down the true final answer, but he accepted my answer when I tried explaining it (he told me "in the interest of time, just explain what you're trying to do"). I ended up passing this, and only got like 2.5 out of 3. Oh yeah, he let me use a really basic calculator.
For the second interview, which took place right after the first guy, the guy was a lot nicer and helped me when I was doing the problem. For example, he told me to use 110 pounds instead of 100, because the math works out nicer, and it did. Here were the questions.
1. Making basic measurements on a cup with a ruler, estimate the volume of it using calculus. After I made my estimate, he had me pour a bottle of water in the cup to test it, and it turns out I overestimated it. He wanted me to explain the reason for the error.
2. Using a bunch of rubber bands to construct a slingshot, how far could you launch a 0.1 kg ball? He wanted to see how I would analyze a situation. Pretty much I modeled the slingshot like a spring and then used basic kinematics for the time when the ball leaves the slingshot. He also wanted me to state reasons why the real answer differs from the theoretical answer.
So I had to have passed both since I didn't get a third interview. For those going for surface or subs, I only knew one guy who needed a 3rd interview for failing one of the first two.
The last interview with Admiral Richardson was the only interview I was seriously nervous for. There's a specific procedure you follow when entering his office. When waking in, as soon as you pass the doorway, you start saying your script, which includes name, hometown, school, and what you're applying for. You're supposed to go straight to the seat, but naturally I froze, finished my script, and then say. He asked me a lot of questions, but his first one was why I wanted to do submarines. His follow up questions were based on what I gave as the final part of my answer. In short, the questions he asked were what I've been doing since graduation, why I didn't finish NROTC, if I had family in the military, and why he should believe that I'm committed to the program. The last question he asked was "What will you bring to the Navy?", and it felt like the most important. He thanked me when it was over and said he'd like to send my dad a letter, and I walked out and then a LCDR congratulated me a few seconds later saying I was accepted.
The type of interview seems to be of a random format. For example, the girl who went before me had to do a report, and another guy was assigned a research paper. We were told that if you get a research paper or book report or just assigned something in general, it's a good thing because it means you're accepted. You just have to do something extra. Well, I didn't get that.
There were about 36 of us, and I believe two were not accepted. From what I understand, those two were applying for instructor/reactors engineer, but were offered a fleet position, and ultimately declined. We filled paperwork out and then at the end, swore in.
That pretty much wraps up the 3 days I was there. I wanted to provide this info since other people have been helpful, and I hope this is helpful as well.