Five Rings Interview ProcessTier 2

Options Market Maker · New York

85 practice questions → Apply at Five Rings → Learn more about Five Rings ↗ Report a question from your Five Rings interview

problems

43 easy 41 medium 10 hard

hires: Quant Trader, Quant Researcher, Software Engineer

Interview funnel

These stages are the quant tracks. Software engineering loops are only mapped where a stage names them.

1 Timed Mental-Math Screen
2 Technical Phone
3 Dice / Betting Game Round (QT)
4 Second Technical Phone (QR)
5 Data Project (QR)
6 Final Rounds

Timed Mental-Math Screen

Five Rings' funnel opens with one brutal filter: a timed mental-math / probability / estimation OA (no calculator, camera on) that is widely failed. There is no coding on it. After the OA, the trader (QT) track goes to 30-second timed math, Fermi estimation, and famously layered game-theory rounds (kangaroo random walks, dice-design puzzles), while the researcher (QR) track leans on distribution theory and inference - those are live interviews, not assessments, so the OA below is the one thing you can drill.

All tracks

current

2023 -> 2027

Mental-Math / Estimation OAtimed, no calculator, camera on~17-20 questions / 17-40 min (2027 trading cycle: 17 min reported)

The signature Five Rings screen: rapid fill-in-the-blank probability, distribution/inference, and calculus-ESTIMATION questions, 30-60 seconds each. The estimation items only want the nearest integer of a fast-growing quantity, so estimate rather than integrate. Take the timed bank below. Candidate report from a 2027 sitting: expect a ~10 second forced pause before each question (so a 60 second question is really ~50), and occasional multi-minute platform stalls mid-test that eat the clock. Do not panic when it happens, it is the test, not you.

Zetamac practice game: free 2-minute arithmetic sprintDefault Zetamac settings, per-operation breakdownPro Mental math for trading interviews: what each firm testsEvery firm screen in one tablePro

Take the timed assessmentReal reported OA questions, on the clockPro

Quant Trader

current

2023 -> 2026

Phone Screen - 30s Timed Mathphone, ~30 seconds each~10 questions

The first phone round (right after the OA): a short behavioral chat, then HR fires roughly 10 rapid questions at ~30 seconds each - nearest integer, no calculator - mixing speed arithmetic, expectation, and Fermi estimation. Same skill as the OA, distinct questions. Drill the timed bank below.

Take the timed assessmentReal reported OA questions, on the clockPro

Unlock the full interview funnel

The first stage is on us — you're seeing it in full. Unlock every later round, the must-do problems, and stage-by-stage prep across all 56 firms with QuantVault Pro.

56 firmsEvery stageMust-do problems

Technical Phone

45–60 min · with a QR / trader Round guide →

Deeper probability and statistics with a quant researcher (often a math PhD who hints heavily): variance of a coordinate of a random point on a sphere, P(X+Y > XY) for two dice, the broken-stick longer-piece expectation, random-walk hitting probabilities, the signature bus-stop residual-life waiting-time problem, and regression facts (Y~X vs X~Y slope bounds, σ_{X+Y} → correlation).

Practice this round 42 problems →

#1237 Variance of a Coordinate on the Unit Sphereseen 2023-10 random-variables easy #72 Bus Waiting Paradoxseen 2023-11 expectation hard #2453 Expected Waiting Time at a Bus Stop (Inspection Paradox)seen 2021-12 stochastic-process hard #2444 Bounds on the Reverse Regression Slopeseen 2021-02 regression easy #2445 Probability That a Dice Sum Beats the Dice Productseen 2021-03 probability easy #2450 Probability That a Stick Broken in Three Forms a Triangleseen 2024-12 probability medium #2465 Expected Distance From Origin After a Planar Random Walkseen 2024-12 stochastic-process medium #2469 Expected Value of the Second-Highest of Several Dice Rollsseen 2025-09 expectation medium

Dice / Betting Game Round (QT)

Interactive · with a trader Round guide →

The trader signature: escalating game-DESIGN problems. Design a custom die (faces summing to 21) to maximize your win rate against an opponent using the same die; then asymmetric-die variants; then die-vs-deck comparisons reasoning about negative covariance from sampling without replacement; plus random-walk EV-bound problems. It's pure EV intuition under rising complexity. Rehearse the muscle with Probability Market-Taking and the free Optiver Beat the Odds sets.

GAME Probability Market-Taking intermediate~12 min Be the price taker on a board of coin, dice and card odds: back the +EV bets, size by Kelly, lock the arbitrag… Pro GAME Next Card intermediate~6 min Call the next card higher or lower and stake part of your bankroll. Count what is left, size to your edge, and… Pro

Practice this round 21 problems →

#2470 Designing Dice to Maximize Win Probabilityseen 2025-11 game-theory hard #316 Three Six-Sided Dice vs One Twenty-Sided Dieseen 2025-11 probability medium #264 Fair Price to Enter a Coin Flip Game expectation easy #921 Deconstructed Cubeseen 2024 combinatorics easy #255 Expected Product of Two Diceseen 2024-01 expectation easy #65 Beating a Loaded Die probability easy #175 Doubling Coin Game: Expected Balance expectation easy #1173 Minimum Match Probability for Biased Dice optimization medium

Second Technical Phone (QR)

45–60 min · estimation / inference Round guide →

The QR second round leans on estimation and inference: MLE for n iid U(0,θ), confidence intervals (normal-unknown-variance vs distribution-free), the 'sum of U(0,1) first exceeds 1' result (E[N] = e) with its variance and CI, mean-vs-median comparisons via Jensen, and geometric-probability problems.

Practice this round 13 problems →

#92 Expected Number of Uniforms to Exceed Oneseen 2023-10 expectation easy #2463 Estimating the Upper Endpoint of a Uniform Distributionseen 2024-06 statistics medium #1370 Comparing Estimators for the Uniform Meanseen 2024-06 statistics medium #2454 Mean Versus Median for a Decreasing Densityseen 2021-01 probability hard #2455 Number of Draws to the First Ace: Mean Versus Medianseen 2021-01 probability easy #2457 Posterior for a Coin Bias After Four Headsseen 2025-08 machine-learning easy #844 Quick Estimation of a Tenth Rootseen 2025-10 statistics medium #2467 Estimating log base 2 of 50 Factorialseen 2021-11 brain-teaser medium

Data Project (QR)

Take-home · NDA Round guide →

A QR-specific take-home dataset project (NDA-covered, so details are scarce). Weak performance here is a common reject reason: it's a real gate, not a formality.

Practice this round →

Editorial round — no practice problems.

Final Rounds

Head of trading → 'boss' Round guide →

The closing sequence: a head-of-trading round and then a 'boss' final. More probability/EV plus fit, with the same friendly-but-high-bar vibe. The full-time bar is reported as brutal.

Practice this round 12 problems →

#739 Expected Longest Heads Streak Across 30 Peopleseen 2024 expectation hard #310 Random Walk to the Boundary of a Squareseen 2024-12 probability hard #370 Expected Area of a Random Triangle on a Unit Circleseen 2025-10 expectation hard #731 Expected Flips to Reach a Head-Tail Boundaryseen 2024 expectation hard #2459 Mean and Variance of a Ratio of Normalsseen 2024-12 random-variables medium #2462 Expected Cover-and-Return Time on a Complete Graphseen 2024-06 stochastic-process hard #2469 Expected Value of the Second-Highest of Several Dice Rollsseen 2025-09 expectation medium #274 Momentum-Switching Tennis Tournament probability hard

The day before

Timed mental-math: arithmetic, log/power approximations, quick probability
Fermi estimation with structured breakdowns
Symmetry/indicator probability + the bus-stop residual-life problem
Dice/betting game DESIGN: distribution thinking, sampling covariance, EV bounds
QR: MLE + CI, E[N]=e, mean-vs-median via Jensen
QR data project: clean EDA + a defensible model

Cheatsheet →

Looking for other firms?

Every firm has a curated interview-questions playlist — a ready-to-drill set of problems matched to how that firm interviews, each with a full worked solution.

Practice every firm's OA: timed replicas, free game replicas and guides in one place →

Drill the Five Rings practice set (85 problems) → Browse all company playlists →

Five Rings round-by-round guides

Five Rings interview guide: the firm, culture, roles and pay →

Stage guides for every firm: superdays · behavioral questions · market-making games

Five Rings interview — FAQ

What is the Five Rings interview process?

Five Rings filters almost solely on a timed mental-math/estimation screen (webcam, ~1-3 min each, no calculator), then technical phone rounds (quant researchers, traders). QT: escalating dice/betting-DESIGN games (custom die, dice-vs-deck covariance, random-walk EV bounds); QR: a data project. Slow replies; brutal full-time bar. The loop runs 6 stages: Timed Mental-Math Screen, Technical Phone, Dice / Betting Game Round (QT), Second Technical Phone (QR), Data Project (QR), Final Rounds.

How many rounds does Five Rings have?

6 stages in total, starting with the Timed Mental-Math Screen and ending with the Final Rounds.

How do I prepare for the Five Rings interview?

Work the stage notes above, then drill the Five Rings interview-questions set and the Five Rings online-assessment practice — each problem has a full worked solution.