Optiver Interview Questions — Page 8

Optiver·Data Scientist·Technical Phone Screen

Jun 2026

Optiver Data Scientist interview with a math-heavy algorithmic problem that looks deceptively like a simulation exercise but punishes you hard if you actually try to simulate it. The whole thing hinges on recognizing a number theory pattern fast enough to implement something logarithmic.

You have two non-empty piles of stones with sizes a and b. Each move, you double the smaller pile by transferring that many stones from the larger one. Determine whether this process will eventually empty one of the piles, or cycle forever. Your solution must run in logarithmic time.

“My first instinct was just to simulate it and slap a visited-states check on top.”

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Optiver·Software Engineer·Technical Phone Screen

Jun 2026

Optiver quant engineer interview threw a classic probabilistic puzzle at me, framed as a Markov chain problem. Pretty standard for this kind of role but the execution under pressure is where things get tricky.

Two ants start at opposite vertices of a regular octagon. Each step, both flip a fair coin and move one edge clockwise or counterclockwise. What is the expected number of flips until they meet at the same vertex or cross on the same edge? You should model this as a Markov chain on the distance between the ants.

“The hint to use a Markov chain on the gap between them is really what unlocks it.”

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Optiver·Data Scientist·Technical Phone Screen

Jun 2026

Optiver Data Scientist interview with a classic probability/random walk puzzle. The kind of question where you either see the structure quickly or spend ten minutes drawing octagons on a whiteboard.

Two particles start at opposite vertices of a regular octagon, four steps apart. Each time step, each particle independently flips a fair coin and moves one step clockwise or counterclockwise. What is the expected number of total coin flips until both particles land on the same vertex?

“The key insight I kept fumbling around before landing on: you can reduce this to tracking the relative gap between the two particles, which itself does a random walk on a cycle.”

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Optiver·Data Scientist·Technical Phone Screen

Jun 2026

Optiver Data Scientist interview with a heavy math/combinatorics problem involving Latin squares. The question was proof-based, which I did not expect for a DS role, and there were follow-ups that pushed into symmetry arguments and edge cases.

You have an n×n Latin square (every row and column is a permutation of 1 through n). Let L be the sum of all entries on or below the main diagonal. Prove that L is at least n(n+1)(n+2)/6, and show a construction that achieves equality.
What is the tight lower bound for the sum strictly below the main diagonal (excluding diagonal cells), and does your equality construction still work?
What is the maximum possible value of L, and how does it relate to the minimum via some symmetry of Latin squares?
Your proof of the lower bound probably only used one of the two permutation constraints (rows or columns). Which one, and does the tightness construction still require both?
How does the argument change if you consider the region on or below the main anti-diagonal instead of the main diagonal?

“I stared at this for a while before anything clicked.”

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Optiver·Data Scientist·Technical Phone Screen

Jun 2026

Optiver data scientist interview with a pretty gnarly market-making game problem spanning five sub-parts. The whole thing was essentially one long quantitative case study dressed up as an interval estimation exercise. Left feeling like I'd passed a math exam I hadn't studied for.

Given a continuous probability distribution over an unknown quantity, how would you set up the optimization problem to choose interval endpoints that maximize expected score in the market-making interval game?
Derive the first-order conditions for the optimal interval and explain how the optimal coverage probability differs between light-tailed and heavy-tailed belief distributions.
How would you allocate risk across five rounds to hit a total score of at least 2.0? Walk through a dynamic programming or heuristic approach and explain how you'd adjust interval tightness based on your running score.
Under a log-normal belief about the true answer, describe a quick mental method for picking near-optimal interval endpoints. How would you adapt this for heavy-tailed beliefs?
How would you design a simulation to validate your five-round interval strategy and estimate the probability of hitting the 2.0 score target?

“This took me a minute to even parse.”

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Optiver·Software Engineer·Technical Phone Screen

Jun 2026

Interviewed for a software engineering role at Optiver and got hit with a graph traversal problem dressed up as a currency conversion puzzle. The constraint that you can't revisit currencies is what makes it interesting, and I did not figure that out fast enough.

Given a list of directional currency exchange rate pairs, find the maximum achievable conversion rate from a source currency to a target currency by chaining exchanges. Paths cannot revisit the same currency, and if the same directed pair appears more than once, use the highest rate.

“My first instinct was Dijkstra but that minimizes, not maximizes, and I lost maybe three minutes mentally fumbling with log transformations before just going with DFS and tracking visited nodes.”

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Optiver·Software Engineer·Technical Phone Screen

Jun 2026

First tech round at Optiver for a Quant Engineer role, and it was pretty much what you'd expect from a trading firm: betting games and EV calculations. Not a coding round at all, more like applied probability under pressure.

You're given a set of betting options. Which one has positive expected value, and how do you prove it?

“The core of the whole round.”

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Optiver·Software Engineer·Online Assessment (OA)

Jun 2026

Optiver software engineer interview with a tree validation problem that looks straightforward until you actually read the constraints carefully. The priority ordering of error codes is where things get interesting and where I think most people trip up.

Given a list of directed edges, determine if they form a valid binary tree. If not, return the first applicable error code from a fixed priority list (INVALID_INPUT, TOO_MANY_CHILDREN, MULTIPLE_PARENTS, CYCLE, MULTIPLE_ROOTS). If valid, return the in-order traversal as a space-separated string, where left/right child assignment follows edge insertion order.

“The core logic isn't that bad.”

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Optiver·Software Engineer·Technical Phone Screen

Jun 2026

Interviewed at Optiver for a software engineering role and got a concurrency-focused coding problem, not a LeetCode-style question. Solved it fine but still didn't move forward because of a background mismatch, which was a bit deflating.

Implement two functions for buying and selling stocks that are safe to use in a multi-threaded environment, meaning stocks cannot be oversold. Use locks to handle the concurrency.

“Not what I expected going in.”

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Optiver·Software Engineer·Technical Phone Screen

Jun 2026

Optiver software engineer interview with a probability and data structures question that had more depth to it than it first appeared. No frills, just math and reasoning under pressure.

You're given a binary search tree where finding node A takes 1 comparison and finding node D takes 3 comparisons. What's the expected number of comparisons to find a uniformly random node? State your assumptions.

“I knew expected value meant summing (probability * cost) over all nodes, but the catch is you only know the depth of two nodes, not the whole tree.”

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