Graviton Research Capital Interview Guide

Topics are probability, permutations and combinations, proof techniques and game theory. Candidates call the questions Brainstellar-style and say the test is harder than at similar firms. Few if any candidates solve every question completely, so partial answers matter. One reported question is a variation of the pirates and coins problem with 2 people, 30 coins and 3 chests. Statistics and financial markets came up in earlier years, but recently finance, competitive programming and CS fundamentals have not been asked, so treat finance content as unlikely.

How to prepare

• Full proofs in 15 to 20 minutes. Practise writing a tidy, complete solution to a medium problem under that clock, and triage by marks before you start.
• The families. Counting methods and advanced counting, pigeonhole and subset-sum arguments, invariants, indicator variables and linearity of expectation, and combinatorial games through the game theory course.
• Sources candidates name. Candidates credit Brainstellar, Mosteller's Fifty Challenging Problems in Probability, Zhou's A Practical Guide to Quantitative Finance Interviews and Crack's Heard on the Street. Our guide to the best books covers the last three.

The format changed. In the 2022 and 2023 seasons it was 2 hard competitive programming problems on HackerEarth in 60 to 75 minutes, and only the 10 to 12 students who solved both were shortlisted. From the 2024 season it is reported as a 1-hour pen-and-paper test of 3 to 5 questions mixing competitive programming with systems questions, answered in pseudocode and logic. Reported systems items: implement concurrent transactions between 2 bank accounts using locks, and remove the branching from a code snippet. Lateral reliability engineers sit a 2-hour HackerEarth test of multiple choice and coding in Python and Bash, and quant tools developers a multiple-choice section on data structures, object-oriented programming and operating systems followed by 2 hard problems, one on the longest common subsequence.

Prepare competitive programming at roughly Codeforces 1700 to 1900, dynamic programming, graphs, trees and bit manipulation, and practise writing it on paper. The C++ internals and concurrency lessons cover the systems half.

Candidates have sent us three problems from Graviton's online coding tests, all in C++ with hidden tests at full size: choose at most M dishes to maximise their total size times their lowest taste, with N up to a million; count the towns on a tree path whose population is at most W, for 200,000 queries; and drop the fewest requests so that two rate limits hold at once. One reported version of the last also had a queue buffer with no service time, so ask how the buffer drains if you get it.

Usually 2 rounds of 45 to 60 minutes with a single interviewer each, though candidates report anywhere from 2 to 5 rounds. The first round is often combinatorics and probability in olympiad style, and the second pure maths, algebra, inequalities and number theory, with proper proofs expected. Saying your reasoning out loud is expected, and taking hints is normal: needing hints on most problems does not cost you the offer.

Reported questions

• Combinatorial games. Alice and Bob remove marbles from a pile of n, each removal no larger than the last and the first removal not the whole pile: who wins for each n? Nim where you take 1 to 6 stones.
• Chessboards. The maximum number of queens that attack nothing, asked more than once in 2026, and the same for rooks, kings and bishops.
• Probability. Two players each toss a coin and cannot see each other; they win if at least one correctly guesses the other's toss. Can they always win? A 7 by 7 symmetric matrix with each column holding 1 to 7: the probability the diagonal holds all of 1 to 7. The probability that two of 100 noodles end up in the same loop when loose ends are tied at random. The probability that the ceiling of X over Y is a perfect square for independent uniforms.
• Markov chains. The probability that HTH appears before HHT in coin tosses, compared by intuition and then by calculation, the expected number of tosses to reach either, and then that expectation conditional on HTH winning.
• Proofs and invariants. Any 200 whole numbers at most 200 contain a subset whose sum is divisible by 200. Eleven soldiers each watch their nearest neighbour: prove one is unwatched. Repeatedly replace two numbers from 1 to 50 by their absolute difference: which final values are possible? Every odd number, by induction.
• Algorithms as puzzles. Find a flag planted at an unknown integer on the real line in time linear in its distance. Lattice paths from the origin to (8, 8) with an even number of direction changes. Search an N by N matrix whose rows and columns are sorted in O(N) time, with the hint to look at a corner (from a quant researcher intern interview).
• Expectation. Linearity of expectation on a random number generator.

Software rounds add probability plus a hard dynamic programming question, a puzzle with operating systems and computer architecture, pointer constness, stack against heap memory, matrix binary exponentiation, and for lateral hires a file explorer built from scratch and log debugging with a binary search over timestamps.

How to prepare

The Markov chain lesson covers the HTH against HHT family in full, and the strategic conditioning lesson the conditional follow-ups. For the games, zero-sum games and minimax and dominance give the winning and losing position method. The Reasoning questions and the probability questions supply the volume.