Question Bank
1042 questions of the kind asked on trading-firm interview loops, every one with progressive hints, a rigorous worked solution, and the interviewer's follow-ups.
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The classic quant interview questions, solved →
Monty Hall, 25 horses, two eggs, the 100 prisoners. Free, every one worked step by step.
Every question with a free worked solution
Probability
- Sum of Seven
- At Least One Six
- Conditioned Die
- Two Red Cards
- Beat My Roll
- The Two-Child Problem
- Monty Hall
- All Different
- The Birthday Paradox
- Gambler's Ruin
- The Hat Check Problem
- The Broken Stick
- Parity Lock
- First Head Wins
- Ace in the Hand
- Socks in the Dark
- The Positive Test
- Highest of Three
- Three Coins, Partial News
- Different Dice
- The Thirteenth Card
- Waiting for the Fill
- The Better Desk
- Three Prisoners
- The Hundred Boxes
- Two Matchboxes
- Hire the Best
- The Random Chord
- Buffon's Needle
- HH Before HT
- Still Waiting
- Which Breaks First
- Calm and Storm
- Two Heads of Evidence
- Above the Threshold
- Fastest of Three
- The Lost Boarding Pass
- Five Reds in a Row
Expected Value
- Price a Die Roll
- Flips to First Head
- Rolls to a Six
- One Reroll Allowed
- Collect All Six Faces
- Expected Maximum
- The St. Petersburg Game
- The Two-Envelope Paradox
- Two Distinct Faces
- Cards Between the Aces
- Lowest of Three Dice
- Same-Color Neighbors
- How Long Does the Rain Last?
- Price the Carnival Dice Game
- Price the Product
- The Longest Streak
- Price a Raffle Ticket
- Balance the Bet
- First the Coin, Then the Dice
- The Press That Breaks
Combinatorics
- Handshakes
- Counting Subsets
- The Round Table
- Trailing Zeros of 100!
- Diagonals of a 12-gon
- Committee With a Quota
- Climbing Ten Stairs
- Strictly Increasing Digits
- Ordered Sums of 10
- Tiling a 2×12 Strip
- Rectangles on a Chessboard
- A Mixed Committee Count
- The Ballot Problem
- One Must Divide Another
- A PIN With a Repeat
- Alternating in a Row
Brainteasers & Logic
- Three Mislabeled Jars
- Clock Hands at 3:15
- Ants on a Triangle
- Burning Ropes
- The 100 Lockers
- The Bridge at Night
- 25 Horses
- The Two Egg Problem
- Twelve Balls, Three Weighings
- Five Pirates, 100 Coins
- Nine Balls, One Heavy
- The Fork in the Road
- Three Switches, One Bulb
- The Round-Trip Average
- Two Trains and a Fly
- Paying With a Gold Bar
- Splitting the Cake
- Three and Five Make Four
- A Fair Toss From a Biased Coin
- One Poisoned Bottle
- One Hundred Hats in a Line
- Ant Across the Cube
- The Banana Caravan
- The Blue-Eyed Islanders
- Strange Dice, Same Sums
- The Light Switch Protocol
- The Last One Standing
- The Last Chip Pays
- Seven Cups, Two at a Time
- The Incompatible Cargo
- The Knight's Round Trip
- Race to Sixty
- The Torn Ledger
- Three Drawers of Chips
- Four Crates, All Lies
- One Question, Foreign Words
Market Making & Betting
- What Does a Market Maker Do?
- Make Me a Market on a Die
- Why Limit a Winning Trader?
- Crossed Market, Two Venues
- Three Odds Formats, One Price
- Maker-Taker Arithmetic
- Market on a Number You Don't Know
- Market on the Product of Two Dice
- The Margin in a Three-Way Line
- How Much Toxicity Can the Rebate Buy?
- Market on the Middle Die
- What Can Tonight Cost?
- Trading Rich to the Basket
- The Unit Trap Market
- Make a Market on Piano Tuners
Statistics
- Estimating the Fleet From Four Serial Numbers
- Carrying the Normal Table
- Halving the Error
- π from Darts
- Method of Moments in One Line
- t or z?
- Long Two, Short Three
- Flows Predict Returns. Or Do They?
- Sizing the Sample for a Target Width
- Correlation Doesn't Care About Units
- Error Bars on a Fill Rate
- Three Sigma Without a Distribution
- Five Bad Days