
Can someone shed light on the interview process at prop shops like Optiver, Flow Traders, All Options, etc?
From what I've researched, I see that the process contains: 1. Mental math test  something like 80 questions in 8 minutes 2. Another quant test based on sequences 3. Another quant test based on puzzles 4. Technical Interview 5. HR Interview
Can someone shed more light on parts 3,4,5 of the above?
Especially, what kind of puzzles are asked in 3, and what sort of questions are asked in the technical interview? Also, how do I prepare for this technical and HR interview?
For 3, I did some research and found some resources to prepare for the puzzle round of firms like GS, JPM for their quant roles. Is the level and type of questions same for Optiver/FT, etc? 




The process for Optiver is a 3part online test, then a phone interview, and finally a superday. Here's the breakdown of the online test:
Part 1: 80 mental math questions in 8 minutes. Questions get progressively harder. An "easy" question would be something like 12 * 9, 11 * 13, 49 * 51, etc. A "medium" question would be 4 * .16, 500 * .005, (2/3) / (2/9). A "hard" question would be 23 * 29, 1002 / 3.
Part 2: Patterns / probability. You will see a sequence of images / numbers and will be asked to fill in the most logical next number / image. You may also be asked some basic probability questions
Part 3: Openended game theory. You will be presented with two longer questions (I think this part was 15 minutes long), and will be asked to come up with an optimal strategy, and explain why it makes sense.
The phone technical interview consists of estimation, probability and expected value. In one situation, I had to approximate 95 / .35 in my head. They are looking for speed and accuracy. During the superday, you will play games against traders and will be asked to explain your strategy / calculations.
Flow Traders is also very heavy on mental math, but it also has a logic test as its second round. It's literally just an IQ test. During the onsite, you will be given a packet and will sit alone in a room for 45 min trying to solve the questions. The questions will require you to make quick calculations and have some financial intuition. Two interviewers will then come in and go through the case with you. I got a bond yield arbitrage case, but I've heard of equity correlation cases as well and even some index arbitrage cases.
Examples of puzzles / games I've encountered during interviews (note that no pencil / paper was allowed for any of these):
1. You are on an island inhabited only by knights, who always tell the truth, and knaves, who always lie. You meet two women who live there and ask the older one, "Is at least one of you a knave?" She responds yes or no, but you do not yet have enough information to determine what they were. So you then ask the younger woman "Are you two of the same type?" She answers yes or no and after that you know which type each is. What type is each?
2. Jane wants to auction off an item but does not know where to go to find bidders. David offers to find bidders for her, but will charge her $10 per bidder he gets to show up. Each bidder will uniformly value the item between [500, 1000]. The highest bidder will win the item and pay the secondhighest bidder's price. How many bidders should jane pay David to find?
3. You have 500 quarters, 500 dimes. You flip all of them. The sum of the values of all coins which were heads up was $95. Give a lower and upper bound on the most likely number of quarters that were heads up. Note: You can narrow it down to two numbers
4. Game A: Roll a die, and get the square of the value. Game B: Roll 2 die, get the product of the values. Game C: Roll 5 die, get the square of the median value. Rank the EV of the games.
5. The game: Flip 200 coins, payout is # of heads. a) Some other people ate bidding to play the game, how much would you bid? b) Only one other bidder  he chooses a bid uniformly at random between 0 and 100. What do you bid? What do you expect to win? c) Ten other bidders, all uniform. What do you bid? What do you expect to win? d) One other bidder, who is perfectly rational. You have the option to tell that person your strategy for bidding. Do you show your strategy, if so what is your strategy? If not, what is your strategy? What is the EV of your strategy? Cant lie.
Note: For part d, the interviewer himself didn't know the best strategy. It was more about talking through the logic. You should be able to get that it's optimal to tell the other person your strategy. Hint: What happens if you tell the other person that you will bid 50 with .5 probability and 0 with .5 probability?
5. 1600 knight in a circular table. Sword given to 1 knight, that knight kills the person to his left and passes the sword to the person after the person just killed. That is, if 4 people in the circle, 1 kills 2, passes to 3, 3 kills 4, passes to 1, 1 kills 3 and the game is over. With 1600 knights, who's the last knight standing?
6. 3 card deck: ace, king, queen. $1 ante each for two players. Each player gets 1 card, third card thrown away. Each player sees their own card. Player 1 can choose to bet an additional $1 or check. If check, then whoever has the higher card takes money in the pot. If bet an additional $1, then player 2 can either fold or call. If fold, player 1 takes pot, if call, then player 2 puts $1 in pot and higher card wins. Optimal strat for player 1?
7. 25 cards taken randomly without replacement from 52 card deck. Create five groups of five cards such that the number of poker hands better than or equal to a straight is maximized. You payoff is the square of the number of such poker hands. E.g., if you're able to create four groups of five that are better than or equal to a straight, your payoff is 16. Create a 6wide market on this game. Hint: Think intuitively, don't try to solve for the exact EV. 



Hey thanks for replying. That was really helpful. For game theoretic questions, how should one go about preparing? Are there some standard books for game theory from which I could solve practice problems or at least get some intuition for it?



