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Example Trading Brain Teasers

Classic interview puzzles asked at firms like Citadel, Jane Street, Flow Traders, SIG, and more — with full worked solutions.

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Trading-firm interviews usually include brain teasers, because they show how you think under pressure: can you reason from first principles, do the mental arithmetic, and stay calm when you're stuck? They also show whether you enjoy solving problems, and how you communicate while doing it.

Below is a small set of brain teasers from our question bank. Each is a real interview question with a full worked solution. Expand it to compare your reasoning, and bookmark any you want to come back to. Ready to start preparing? Full access unlocks 600+ questions plus progress tracking.

Sample Questions & Solutions

Each question is a real interview problem. Try it yourself first, the full solution is revealed below.

Q1

Fox vs. Duck

Medium
A duck is swimming at the center of a circular lake. A fox is waiting at the shore, unable to swim and eager to eat the duck. It may move around the whole lake with a speed four times faster than the duck can swim. As soon as the duck reaches the surface, it can fly, but not while still in the lake.

Can the duck always reach the shore without being caught by the fox?
Show solution
At a radius of slightly less than $\frac{r}{4}$, the duck can swim in circles, forcing the fox to run around.

Fox vs Duck

Once the duck is at an angle of $\pi$ from the fox, it starts swimming towards the shore.
  • The duck has to cover a distance of $\frac{3r}{4}$
  • The fox has to cover a distance of $\frac{2\pi \cdot r}{2}$
Fox vs Duck

Since the fox moves four times faster, the distance of the fox has to be larger than four times the distance of the duck.

As we can see, \begin{equation}\frac{3r}{4} * 4 < r* \pi \end{equation} \begin{equation} 3r  < 3.14r \end{equation} \begin{equation} 3  < 3.14 \end{equation} Therefore, the duck will survive!
Asked at: Flow Traders IMC Da Vinci All Options Maven Mako Citadel Securities Virtu DRW
Category: Logical View full question page →
Q2

Pirates Dividing a Treasure

Medium
Five pirates need to divide 100 coins. The pirates have a hierarchy, from level 1 to level 5. The pirate with the highest seniority has level 5 and the pirate with the lowest seniority has level 1. The pirate with the highest seniority proposes a division plan and all the pirates vote on it. If at least 50% of the pirates agree on the plan, the coins will be divided according to the proposal. If not, the highest senior pirate is kicked from the ship, and the next senior pirate may propose a plan. This process continues until a proposal is accepted. All pirates are extremely smart and extremely greedy.

How does Pirate #5 divide the treasure in order to survive and maximize his coin count? What will his coin count be?
Show solution
  • To understand the answer, we need to reduce this problem to only two pirates. Pirate #2 represents 50% of the votes in this case, so he can easily propose that he gets all the 100 coins.
  • Now increase the problem to three pirates. Pirate #3 knows that if his proposal does not get accepted, that Pirate #2 will get all the coins and Pirate #1 will be left with nothing. Therefore, he decides to bribe Pirate #1 with one coin. Pirate #1 knows that one gold coin is better than nothing, so he has to vote for Pirate #3. Since Pirate #1 and Pirate #3 will vote for it, it will be accepted.
  • If there are four pirates, pirate #4 needs to get one more pirate to vote for his proposal. Pirate #4 realises that if he dies, Pirate #2 will be left with nothing (according to the proposal with 3 pirates) so he can easily bribe Pirate #2 with one coin to get his vote. With two votes and four pirates, the proposal will be accepted.
  • Now increase the problem to five pirates. Pirate #5 needs two votes and he knows that if he dies, Pirate #1 and Pirate #3 will get nothing. He can easily bribe Pirate #1 and Pirate #3 with one coin each to get their vote. In the end, he proposes, from Pirate #5 - Pirate #1:{98, 0, 1, 0, 1}This proposal will get accepted and will provide the maximum amount of gold to Pirate #5.
Asked at: Flow Traders Virtu DRW
Category: Simplification View full question page →
Q3

The King's Party

Medium
Someone breaks into the wine cellar of a king, where he stores 1000 bottles of wine. This person proceeds to poison one of the 1000 bottles, but gets away too quickly for the king's guard. Nobody knows which one he poisoned. The king needs the remaining 999 safe bottles for his party in four weeks. The king has ten prisoners who deserve execution. The poison takes just less than four weeks to take effect. Any amount of the poisoned wine will kill whoever drinks it.

How can he figure out which bottle was poisoned in time for the party?
Show solution
Since every prisoner can end up dead or alive, there are 2^10 = 1024 possible outcomes. Since 1024 > 1000, it's actually possible to use an approach using binary strings.
  • The king assigns each servant a number from 1 to 10.
  • The king assigns each bottle a number from 0 to 999.
When he labels them, he writes the number on the bottle in binary with ten digits, like this:
  • 0: 000000000
  • 1: 000000001
  • 2: 000000010
  • 3: 000000011
  • 4: 000000100
  • ...
  • 999: 1111100111.
The strategy is simple: the king assigned the prisoners a number from 1 to 10, indicating the position of the number in the binary string. If the string has a number one on the, for example, fifth and sixth position, then the prisoners with number five and six have to drink the wine. After less than four weeks, suppose only prisoners number five and six die. This means the binary representation of poisoned wine has a '1' at position five and six, and the rest are all zeros.

Convert this binary number to a decimal and that gives you the number of the poisoned wine.
Asked at: Flow Traders Maven Citadel Securities Virtu DRW
Category: Out of the Box View full question page →

Why practise these

The hard part isn't any single skill, it's doing all of them at once. You have to spot how to set the problem up, keep talking so the interviewer can follow your reasoning, and get to a clean number without fumbling, all while the clock runs. Each part is easy alone and much harder combined, and that only smooths out with reps. That's what working through these builds: after enough of them, you start recognising a problem's structure before you've finished reading it, which is exactly the composure that's hard to fake in the room.

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