Problems

118 curated questions across 15 topics, each with hints and a worked solution, including at 24 firms.

– of 118 solved

Easy –/53Medium –/52Hard –/13

/

69 results

Probability & Combinatorics

Medium#1
Waiting for Two Heads in a Row
Goldman Sachs · Morgan Stanley · Two Sigma
Probability · Numerical · 8 min
Easy#3
Birthday Problem Threshold
Probability · Numerical · 5 min
Easy#4
At Least One Boy
D. E. Shaw
Probability · Multiple choice · 3 min
Medium#5
Monty Hall with Four Doors
Probability · Numerical · 6 min
Easy#6
Positive Test, Rare Condition
Probability · Numerical · 5 min
Medium#48
Which Coin Did I Draw?
Jane Street
Probability · Numerical · 6 min
Easy#50
An Even Number of Heads
Jane Street
Probability · Numerical · 3 min
Easy#58
P(X > Y) for Two Normals
Citadel
Probability · Numerical · 3 min
Medium#61
Best of Three or Win by Two?
Susquehanna (SIG) · Optiver
Probability · Multiple choice · 6 min
Easy#65
Will the Next Card Be Higher?
Susquehanna (SIG)
Probability · Numerical · 4 min
Easy#66
Three Dice in Increasing Order
Optiver
Probability · Numerical · 3 min
Hard#68
Break the Longer Piece
Goldman Sachs
Probability · Numerical · 12 min
Easy#71
First to Roll a Six
J.P. Morgan
Probability · Numerical · 4 min
Easy#78
A Sum of 4 Before a Sum of 2
Goldman Sachs
Probability · Numerical · 3 min
Medium#79
Product of Two Uniforms Below One Half
Goldman Sachs
Probability · Numerical · 6 min
Easy#94
One Double-Headed Coin in a Thousand
Goldman Sachs · Squarepoint Capital · Renaissance Technologies
Probability · Numerical · 4 min
Easy#109
A Negative Test with No Base Rate
D. E. Shaw
Probability · Free response · 4 min
Easy#113
Three Flips, at Least One Head
Akuna Capital
Probability · Numerical · 3 min
Easy#118
Real Roots from Random Coefficients
Bank of America
Probability · Numerical · 4 min

Statistics & Statistical Inference

Easy#7
Is the Coin Fair?
Statistics · Numerical · 4 min
Medium#8
Why Divide by n − 1?
Statistics · Free response · 12 min
Easy#76
Uncorrelated but Not Independent
Two Sigma
Statistics · Free response · 5 min
Medium#87
Range of the Third Correlation
Citadel
Statistics · Multiple choice · 6 min
Medium#89
Best Guess from a Noisy Signal
Citadel · Susquehanna (SIG)
Statistics · Numerical · 6 min
Easy#90
Mean of a Lognormal
Citadel
Statistics · Numerical · 3 min
Medium#92
Duplicating Your Regression Data
Point72 · J.P. Morgan
Statistics · Multiple choice · 5 min
Easy#95
At Least 220 Heads in 400 Flips
Goldman Sachs · Squarepoint Capital
Statistics · Numerical · 4 min
Easy#101
Best-Fit Line Through Three Points
Squarepoint Capital
Statistics · Numerical · 4 min
Easy#117
Correlated Predictors in a Regression
Two Sigma
Statistics · Free response · 5 min

Expected Value & Decision Theory

Medium#10
Roll Once, Maybe Reroll
Citadel · Jane Street · Squarepoint Capital
Expected Value · Numerical · 6 min
Easy#11
Hats Returned at Random
Expected Value · Numerical · 4 min
Easy#12
Kelly Bet on a Biased Coin
Expected Value · Numerical · 5 min
Medium#47
Die Game with Two Rerolls
Jane Street · Susquehanna (SIG)
Expected Value · Numerical · 6 min
Easy#51
The Advantage of Flipping First
Jane Street
Expected Value · Numerical · 4 min
Easy#63
Accepting a Doubled Bet
Susquehanna (SIG)
Expected Value · Numerical · 4 min
Easy#64
Even Faces Pay Double
Susquehanna (SIG)
Expected Value · Numerical · 5 min
Easy#75
Twenty per Head or Five Hundred for Four
Akuna Capital
Expected Value · Multiple choice · 3 min
Easy#81
Paid for Every Point Over Ten
DRW
Expected Value · Numerical · 5 min
Easy#98
Expected Gap Between Two Dice
Jane Street
Expected Value · Numerical · 3 min

Brain Teasers & Logic

Medium#14
Four Crossers, One Lamp
Brain Teasers · Numerical · 8 min
Easy#15
Measuring 45 Minutes with Two Ropes
Brain Teasers · Free response · 6 min

Mental Math & Estimation

Easy#17
47 × 53 in Your Head
Mental Math · Numerical · 1 min
Easy#18
Estimate √50
Mental Math · Numerical · 2 min

Market Making & Trading Games

Medium#19
Make a Market: Three Dice
Market Making · Market making · 10 min
Hard#20
Make a Market: Five Cards
Market Making · Market making · 15 min
Medium#21
Fair Value of the Higher Die
Jane Street
Market Making · Numerical · 5 min
Easy#22
Why Widen Your Spread?
Market Making · Multiple choice · 4 min
Medium#114
A Guaranteed Bet on Three Horses
Susquehanna (SIG)
Market Making · Numerical · 5 min

Stochastic Processes & Markov Chains

Medium#23
Gambler's Ruin with an Edge
Stochastic Processes · Numerical · 10 min
Easy#62
One Dollar Against Two
Susquehanna (SIG)
Stochastic Processes · Numerical · 5 min
Hard#86
Will the Amoebas Die Out?
Morgan Stanley
Stochastic Processes · Numerical · 10 min
Easy#107
Up Ten Before Down Five
Five Rings
Stochastic Processes · Numerical · 3 min

Stochastic Calculus

Medium#25
Differential of W²
Stochastic Calculus · Multiple choice · 4 min
Medium#26
Expected Exponential of Brownian Motion
J.P. Morgan
Stochastic Calculus · Numerical · 5 min
Medium#27
Show W² − t Is a Martingale
J.P. Morgan
Stochastic Calculus · Free response · 10 min
Medium#69
Hit +1 Before −2
Morgan Stanley · Credit Suisse
Stochastic Calculus · Numerical · 6 min
Medium#70
Which Powers of W Are Martingales?
Morgan Stanley
Stochastic Calculus · Multiple choice · 5 min
Medium#73
Making W³ a Martingale
J.P. Morgan
Stochastic Calculus · Multiple choice · 6 min

Derivatives Pricing & Greeks

Easy#28
Put–Call Parity
Derivatives · Numerical · 3 min
Medium#29
Pricing an At-the-Money Call
Derivatives · Numerical · 6 min
Easy#30
Greeks Near Expiry
Derivatives · Multiple choice · 4 min
Hard#31
Implied Volatility by Bisection
Derivatives · Coding · 20 min
Medium#116
Interest Rates and Early Exercise
Two Sigma
Derivatives · Free response · 6 min

Fixed Income & Interest Rate Models

Easy#32
Price a Two-Year Coupon Bond
Fixed Income · Numerical · 4 min
Medium#33
Modified Duration of a Zero
Fixed Income · Numerical · 4 min
Medium#34
The One-Year Rate, One Year Forward
Fixed Income · Numerical · 5 min

Linear Algebra & Optimization

Medium#35
Two-Asset Minimum-Variance Portfolio
Morgan Stanley
Linear Algebra · Numerical · 6 min

Python / C++ Quant Coding

Medium#42
EWMA Volatility Filter
Quant Coding · Coding · 10 min

Numerical Methods & Monte Carlo

Hard#45
Monte Carlo European Call
Numerical Methods · Coding · 20 min