The 47 classic quant interview questions
Every trading interview draws on the same small canon of famous problems. Monty Hall, the 25 horses, two eggs and a hundred floors, the prisoners and their boxes. They recur because each one has a trick worth testing: a symmetry to spot, an invariant to find, a piece of information that looks decisive and is not.
All of them are collected here, every one worked step by step, with the follow-up questions an interviewer asks once you land the answer. Free to read, no account needed. If you can do these cold, you have cleared the folklore and the real work starts in the full bank.
Probability
- The Monty Hall problemMediumalso: the three doors problem · should you switch doors
- The birthday problemMediumalso: shared birthday paradox · how many people for a shared birthday
- The gambler's ruin problemMediumalso: random walk ruin probability
- The hat check problemMediumalso: the derangement problem · probability nobody gets their own hat
- The broken stick problemHardalso: probability three pieces form a triangle
- Simpson's paradoxMediumalso: the reversal paradox · when aggregated data contradicts every subgroup
- The three prisoners problemMediumalso: the three prisoners paradox
- The 100 prisoners problemHardalso: 100 prisoners and 100 boxes · the cycle-following strategy
- The Banach matchbox problemHardalso: the two pockets problem
- The secretary problemHardalso: the 37 percent rule · the optimal stopping problem
- Bertrand's paradoxHardalso: the random chord problem · probability a chord is longer than the side of the triangle
- Buffon's needle problemHardalso: estimating pi by dropping needles
- Penney's gameMediumalso: expected flips to see HH versus HT · why waiting times for patterns differ
- The two heads coin problemMediumalso: Bayes with a double headed coin
- The airplane seat problemMediumalso: the lost boarding pass problem · 100 passengers and 100 seats
Expected Value
- The dice reroll problemMediumalso: expected value with one reroll · rolling a die with the option to roll again
- The coupon collector problemMediumalso: expected rolls to see all six faces
- Expected maximum of two diceMediumalso: expected value of the higher roll
- The St. Petersburg paradoxMediumalso: the infinite expected value game
- The two envelopes problemHardalso: the exchange paradox
- The longest run of headsHardalso: expected longest streak in coin flips
Combinatorics
- Trailing zeros of 100 factorialMediumalso: how many zeros at the end of 100! · counting factors of five
- Domino tiling of a 2 by n boardMediumalso: the Fibonacci tiling problem
- How many rectangles on a chessboardMediumalso: counting rectangles in a grid
- The ballot problemMediumalso: the reflection principle · probability one candidate is always ahead
Brainteasers & Logic
- The burning rope problemMediumalso: measuring 45 minutes with two ropes · the fuse puzzle
- The 100 lockers problemMediumalso: the 100 doors puzzle · which lockers stay open
- The bridge crossing problemMediumalso: four people one torch · the bridge and torch puzzle
- The 25 horses puzzleHardalso: 25 horses and 5 tracks · finding the fastest three horses
- The two egg problemHardalso: the egg drop puzzle · 100 floors and two eggs
- The 12 balls problemHardalso: twelve coins in three weighings · finding the odd ball
- The five pirates problemHardalso: pirates and 100 gold coins · the pirate game
- The water jug problemMediumalso: measure 4 litres with a 3 and 5 litre jug · the Die Hard jug puzzle
- Fair coin from a biased coinMediumalso: the von Neumann trick · simulating a fair toss with a biased coin
- The poisoned wine problemMediumalso: 1000 bottles and 10 testers · finding the poisoned bottle
- The 100 hats problemMediumalso: the prisoners and hats puzzle · hat colour guessing strategy
- The ant on a cube problemMediumalso: shortest path across a cube
- The camel and bananas problemHardalso: the banana transport puzzle
- The blue eyes puzzleHardalso: the blue-eyed islanders problem · the common knowledge puzzle
- Sicherman diceHardalso: relabelled dice with the same sums
- The 100 prisoners and a light bulb problemHardalso: the light switch puzzle
- The Josephus problemMediumalso: the circle elimination puzzle · every second person eliminated
- The knight's tour problemMediumalso: closed knight tour on an odd board
- The game of NimMediumalso: the three heaps game · nim strategy with XOR
- The mislabelled boxes problemMediumalso: all labels wrong puzzle
- The two guards one question puzzleMediumalso: the unknown words riddle
Statistics
The classics are the warm-up
Interviewers know these are public, so the ones that decide an offer are the questions you have never seen. That is the rest of the bank: hundreds of original problems, written for QuantPit, with timed company-style screens to run them under pressure.