Tag Interview Brain Teasers

Brain teasers you might encounter in a finance, consulting, or engineering interview

5 Quant Brain Teasers

Whether you’re preparing for an interview or just trying to keep your mind sharp, here are some quant brain teasers to test your skills.

Remember, if you get a brain teaser at an interview, you don’t necessarily need to get the correct final answer to do well, you just need to demonstrate your problem-solving skills, your ability to think and communicate, and your comfort with math, logic, and statistics. For more tips on tackling brain teaser interviews, check out our guide to brain teaser interview questions.

1. Friday the 13ths

Easy-medium difficulty

What is the minimum and maximum number of Friday the 13ths that can occur in a calendar year?

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Prison Keys Strategy

A prison warden was feeling capricious and played a game with the prison keys:

  1. Each prisoner is handed a key to another prisoner’s cell.
  2. Each prisoner will know which other prisoner was initially given the key to their cell (but does not know whose key they were handed).
  3. Each day, when all prisoners are out of their cells and no one is watching, each prisoner is allowed to place keys in another prisoner’s cell.
  4. Each night, each prisoner can collect any keys placed in their cell.
  5. The prisoners can summon the warden when they’re sure everyone has their own key – but if they are wrong, they’re immediately executed.
  6. The prisoners can discuss a strategy beforehand but cannot communicate in any way after keys are handed out.

What is the fewest number of days it would take for the prisoners to be sure everyone has their key? What was the strategy to achieve this?

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Sharing Game Theory Puzzle

In this sharing game theory puzzle, 3 friends take turns taking from a jar of 1000 candies to share. For example, the 1st friend could take 500 candies, then the 2nd friend could take 400, and the 3rd friend would take the remaining 100.

No one wants to be seen as greedy, but no one wants to end up with the fewest candies either. As such, their goals are (in order of preference):

  1. Do not end up with the most candies, nor the fewest candies (a tie for most or fewest also fails this condition)
  2. End up with as many candies as possible

All of them are logical, rational, know each other’s goals, but cannot communicate before or during sharing. How many candies should each friend end up with?

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Russian Roulette Riddle

In the morbid game of Russian Roulette, a partially loaded revolver with a six-chamber cylinder is randomly spun, pointed at one of the players, and fired. If the revolver landed on an empty chamber, the lucky player is safe, and the process is repeated with the next player. The obvious objective of the game is to not get shot.

You find yourself stuck in a game of Russian Roulette. A freshly loaded revolver is aimed at the first player, and it turns out to be an empty chamber. Your turn is next, and you are given the choice to either:

  • Spin the cylinder before pulling the trigger (i.e., you get a random new chamber)
  • Or just pull the trigger (i.e., let the revolver fire whatever is in the next chamber)

Which choice should you pick if the revolver was originally:

  1. Loaded with one bullet?
  2. Loaded with bullets in two random chambers?
  3. Loaded with bullets in two consecutive chambers?

Assume the revolver cannot misfire, and that spinning the cylinder lands on all chambers with equal probability.

Some variation of this Russian Roulette riddle was once asked in interviews at Jane Street, Susquehanna International Group (SIG), Facebook (now Meta), UBS, Capital One, and more.

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The Impossible Puzzle

This puzzle was coined the “Impossible Puzzle” by Martin Gardner, a famous math and science writer that liked to create and write about math games and puzzles. The puzzle is named as such because it appears to provide insufficient information to solve, but it is in fact solvable! Read on for the puzzle and the (very difficult) solution.

There are two distinct whole numbers greater than 1, we can call them x and y (where y > x). We know the sum of x and y is no more than 100.

Sam and Prada are perfect logicians. Sam (“sum”) is told x + y and Prada (“product”) is told x * y, and both of them know all the information provided so far.

Sam and Prada have this conversation in which they truthfully deduce the numbers:

  1. Sam: I know Prada does not know x and y.
  2. Prada: Well now I know x and y.
  3. Sam: Ah, now I also know x and y.

Can you figure out x and y using this information?

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Reroll the Die

Suppose there is a game in which you roll a fair, 6-sided die and win dollars equal to the outcome of the roll. How much would you expect to win on average?

Suppose, if you don’t like the outcome of the roll, you can reroll the die once, and win dollars equal to the outcome of the 2nd roll (once you choose to reroll, you can no longer go back to the 1st roll). How much would you expect to win on average?

Suppose, if you don’t like the outcome of the 2nd roll, you can reroll the die once more, and win dollars equal to the outcome of the 3rd roll (once you choose to reroll, you can no longer go back to previous rolls). How much would you expect to win on average?

This was an actual brain teaser question once asked at Jane Street for an interview for an intern role.

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