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# 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 difficulty

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

## 2. Russian Roulette Riddle

Medium difficulty. This quant brain teaser was once asked at a Jane Street interview.

In Russian Roulette, a 6-chamber revolver is partially loaded. The revolver is randomly spun, and then fired at a player.

You are stuck in a game of Russian Roulette. The revolver is freshly loaded, spun, and fired at the first player – the chamber is empty. 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 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:

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.

## 3. Reroll the Die

Easy difficulty. This quant brain teaser was once asked at a Jane Street interview.

In this game, you roll a fair 6-sided die and win dollars equal to the outcome.

You can roll the die once, and you can either (1) keep the outcome or (2) choose to reroll once. If you reroll, you are stuck with the 2nd roll’s outcome. How much would you expect to win on average?

How about if you get 3 roll opportunities? I.e., roll once, if you don’t like the outcome, you can roll a 2nd time, and if you don’t like the 2nd outcome, you can roll a 3rd time.

## 4. Tennis in 2 or 3 sets

Easy difficulty. This quant brain teaser was once asked at a D. E. Shaw interview.

In a best-of-3 tennis match, the first player to win 2 sets wins the match. Is it more likely for a best-of-3 tennis match to end in 2 or 3 sets?

## 5. Wrong Seat Probability

Hard difficulty

There is a fully-booked flight with 100 seats. The first person decides to ignore the seat assignments, and sits in a random seat. Each subsequent person sits in their assigned seats if available, or sits in a random unoccupied seat if not.

What is the probability that the last person happens to find their assigned seat unoccupied?

Need more practice? Here are 7 more quant interview questions you could encounter.