Interview Brain Teasers

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

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Brain Teasers and Puzzles

Impossible Sudoku

You may be familiar with Sudoku, a combinatorial number placement puzzle in which you fill in a 9×9 grid with digits such that each row, column, and 3×3 square contains all of the digits 1-9 exactly once.

You come across a Sudoku puzzle in which the initially populated numbers appear to be legal (no row, column, or square had the same number twice), but it is clear that trying to solve the puzzle would lead to an impossible arrangement of numbers – an unsolvable puzzle not because there is not enough information, but because it forces you into a contradictory/rule-breaking result. What is the smallest possible sum of the initial numbers?

More info and solution “Impossible Sudoku”
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Brain Teasers and Puzzles

Pirate Survivor Puzzle

The democratic pirates are at it again! Since last time, they have become very successful and have now expanded to 100 pirates. They decide this is too large of a group for plundering, so true to their democratic roots, they want to settle it with a vote:

  1. They vote on whether to kick out the newest (least senior) pirate.
  2. If a majority votes “aye”, then the newest pirate is kicked out, and the process repeats with the remaining pirates.
  3. If half or more of the remaining pirates vote “nay”, then the vote is over and everyone remaining is safe.

Each pirate wants to stay in the group, but if that is assured, they would prefer to kick out as many other pirates as possible (fewer ways to split the treasure).

How many pirates will remain at the end of this process?

More info and solution “Pirate Survivor Puzzle”
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Brain Teasers and Puzzles

Handshake Puzzle

Hasan and Lauren attended a dinner party with 4 other couples. Since some people already knew some of the other guests, every person at the dinner party shook hands with every person they had not met before.

Lauren noticed that everyone else (excluding Lauren herself) ended up with a different number of handshakes!

Can you figure out how many people Hasan shook hands with?

More info and solution “Handshake Puzzle”
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Brain Teasers and Puzzles

Majority Vote Puzzle

After the results of an election, you are told that one candidate has received the majority of the votes, but you don’t know which candidate. You have exactly one opportunity to hear the votes, but:

  • The list of votes is very long
  • The votes will be announced one after another in random order
  • You have a poor memory (can only remember a couple of names or numbers)
  • You are not allowed to write or record anything

Given these restrictions, is there a way figure out which candidate received the majority of votes?

More info and solution “Majority Vote Puzzle”
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Brain Teasers and Puzzles

Equal Piles of Face-up Cards

There is a standard deck of cards, with some cards face-up and the rest of the cards face-down. You are told exactly how many cards are face-up, but you are not allowed to look at the cards.

Without seeing which cards are face-up and which are face-down, how can you divide the deck into two piles of cards that contain the same number of face-up cards?

More info and solution “Equal Piles of Face-up Cards”
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Brain Teasers and Puzzles

Same Place Same Time

You spend an entire day hiking up a mountain, and camp overnight at the top. The next day, you hike down the mountain along the same trail, starting around the same time you started the day before.

How likely is it that there is a point on the mountain that you passed at the exact same time on both days?

More info and solution “Same Place Same Time”
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Brain Teasers and Puzzles

Tale of Two Trains

There are two trains that run between two cities. The trains are identical and run on identical routes, so passengers have no preference between the two and would take whichever train that pulls into the station. The trains run at the same frequency: exactly once an hour.

You often travel between the two cities on a whim, and when you do so, you show up at the station at a completely random time. Yet after many trips over the years, you notice that you have taken one of the trains three times as often as the other. Is this just really bad/good luck, or is there another likely explanation?

More info and solution “Tale of Two Trains”
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Brain Teasers and Puzzles

Moving Battleship Puzzle

You are trying to hit a moving battleship, but you have no way of monitoring its position. However, you have the following information:

  • You know where the battleship started.
  • You know when the battleship started moving.
  • You know the battleship is only moving along a straight line.
  • You know the battleship moves a constant speed per hour, and that speed is an integer. But you do not know what that speed is.

Every hour, you can fire precisely once at any point on that line. Is there a strategy you can use that will guarantee you will hit the battleship in a finite amount of time?

Fun fact, this was an actual brainteaser given to me in the second round interview for a hedge fund internship back in 2011.

Preparing for a brain teaser interview? Check out our ultimate guide to brain teaser interviews.

More info and solution “Moving Battleship Puzzle”
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Brain Teasers and Puzzles

Odd Hourglasses

You have two odd hourglasses: one that times exactly 4 minutes and one that times exactly 7 minutes. What is the best way to measure exactly 9 minutes using just these two hourglasses?

More info and solution “Odd Hourglasses”
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Brain Teasers and Puzzles

Four Digits Squared

Which perfect square of a 4-digit number has the same last four digits as the original number?

More info and solution “Four Digits Squared”
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Brain Teasers and Puzzles

Arrange the Digits

There are 362,880 different ways to arrange the digits 1 through 9 into a 9-digit number. How many of these combinations are prime numbers?

More info and solution “Arrange the Digits”
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Brain Teasers and Puzzles

Deducing Bicycle Spokes

A bicycle shop has some unique bicycles. Each bike is identical, and each bike’s front and back wheels has at least one spoke each. You don’t know how many bicycles are in the shop, but you know there are between 200 and 300 spokes in total.

If you knew the exact number of spokes, you would be able to figure out the number of bicycles.

You don’t know the exact number of spokes, but just knowing the fact that you would be able to figure it out with that information allows you to deduce the answer. How many bicycles and spokes are there?

More info and solution “Deducing Bicycle Spokes”
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Brain Teasers and Puzzles

Guess the Playing Cards

There are three playing cards in a row.

There is a heart to the left of a diamond. There is a five to the right of a jack. There is a club to the left of a diamond. There is a queen to the left of a club.

What are the three cards?

More info and solution “Guess the Playing Cards”
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Brain Teasers and Puzzles

5 Pirates Puzzle

Five pirates are figuring out how to divide up a newly plundered treasure of 100 gold coins. From most senior to least senior: Pirate A, Pirate B, Pirate C, Pirate D, and Pirate E. The rules:

  1. The most senior pirate must propose a distribution (for example, giving himself all 100 gold coins and 0 for everyone else), and then all the pirates must vote on it.
  2. If at least half of the pirates vote for a proposal, the proposal is accepted and the gold is split according to that distribution.
  3. Otherwise, if the proposal is rejected, the pirate that proposed it is kicked out, and this process repeats with the remaining pirates.
  4. Each pirate’s main goal is to maximize the gold they receive (but a pirate that is kicked out gets no gold), but are also spiteful enough to prefer kicking out the other pirates, all else equal. The pirates are also distrustful of each other and will not make any side deals, so the distribution of an accepted proposal is final.

What is the greatest number of coins that Pirate A can distribute to himself?

This is a classic logic puzzle, occasionally encountered in tech interviews many years ago.

Preparing for a brain teaser interview? Check out our ultimate guide to brain teaser interviews.

More info and solution “5 Pirates Puzzle”
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Brain Teasers and Puzzles

Wrong Seat Probability

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?

More info and solution “Wrong Seat Probability”
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Brain Teasers and Puzzles

Chance of Rain

You are driving to Seattle to meet some friends, and want to know whether you should bring an umbrella. You call up 3 of your friends who live there and independently ask them if it’s raining. Your friends like to mess with you, so each of them has a 1/3 chance of lying. If all 3 friends tell you it is raining, what is the probability it is actually raining there?

This question was asked in an actual Facebook data scientist/data analytics interview.

Preparing for a brain teaser interview? Check out our ultimate guide to brain teaser interviews.

More info and solution “Chance of Rain”
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Brain Teasers and Puzzles

Game the Coin Flip Game

A small company is losing money and the boss is looking for ways to cut costs. The boss is a foolish gambler, so he offers two employees the choice of either taking flat 10% pay cut, or playing the following coin flip game for each paycheck:

  1. The employees each flip a fair coin – 50% heads and 50% tails; the boss will ensure they are not pulling any tricks.
  2. They can see their own outcome but not the outcome of the other employee’s coin flip. They must then guess the outcome of the other employee’s coin flip.
  3. If at least one of them guesses correctly, they get their full paycheck.
  4. If both of them guess incorrectly, they get nothing.

The two employees take some time to work out a strategy, and then confidently accept the offer to play the coin flip game.

What strategy did they come up with that made them confident the coin flip game will give them more money?

More info and solution “Game the Coin Flip Game”
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Brain Teasers and Puzzles

Secret Translation

The CIA intercepted some messages from a criminal organization, some in English and some in an unknown foreign language or code. As a CIA analyst and translator, you have figured out the following sentences and their English translations, but you do not yet know which sentence matches which translation:

  • Casara ashter osar
  • Intara amar
  • Intara orter osar
  • Alatara inter osar
  • Ortara amar
  • Alatara orter osar
  • I see a spy
  • I run
  • You see me
  • You see a spy
  • A suspicious man sees an enemy
  • You run

You have the opportunity to send a message in order to provoke a reaction from the criminal organization. Can you figure out and match up the translations above, and then send a message saying “a suspicious man runs” in this foreign language?

More info and solution “Secret Translation”
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Brain Teasers and Puzzles

Bribing a Series of Guards

A criminal is planning an escape across a well-guarded bridge, which has a series of 9 guards, who each require a bribe of one coin in order to pass by them in either direction.

The criminal can keep a stash of coins in the area before the guards and between each guard. However, he can only carry 4 coins when approaching or passing any guard, in order to remain stealthy and not alert the other guards.

For example, if he starts with 6 coins, he can bring 4 with him to bribe the first guard, and end up with 3 coins in between the first and second guards.

How many coins does the criminal need to bring to the bridge in order to successfully pass by all 9 guards?

More info and solution “Bribing a Series of Guards”
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Brain Teasers and Puzzles

Flipping Every N-th

There are 100 face-down cards. The first person that passes by flips over every card, the 2nd person that passes by flips over every 2nd card, and so forth – the n-th person that passes by flips over every n-th card. Before you know it, 100 people have passed by.

After all 100 people have passed by, which cards are face-up and which are face-down?

Fun fact, this was an actual brainteaser given to me in the first round interview for a hedge fund internship back in 2011.

Preparing for a brain teaser interview? Check out our ultimate guide to brain teaser interviews.

More info and solution “Flipping Every N-th”
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Brain Teasers and Puzzles

Street Number Puzzle

You were walking around on a major street with 5-digit street numbers (for example, 11213) and noticed one of the street numbers was special – any two consecutive digits formed a 2-digit perfect square (in the order the digits appeared in the original number).

What number was it?

More info and solution “Street Number Puzzle”
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Brain Teasers and Puzzles

Rigging a Vote

There are five candidates participating in an unusual election. There are four rounds of voting, and only two candidates participate in each round, with the winner moving on and the loser dropping out. This means first candidate 1 will run against candidate 2, then the winner will run against candidate 3, and so on, with the winner of the last round being elected.

Polling shows that Stephen Hawking is not very popular. There are five equal-sized groups in the voting population, and polling shows they prefer the candidates in the following order:

  • Group 1: Einstein > Newton > Maxwell > Hawking > Curie
  • Group 2: Newton > Curie > Maxwell > Einstein > Hawking
  • Group 3: Curie > Maxwell > Einstein > Newton > Hawking
  • Group 4: Einstein > Newton > Hawking > Curie > Maxwell
  • Group 5: Newton > Maxwell > Einstein > Hawking > Curie

But Hawking has a secret weapon – he gets to choose the order the candidates participate in each round.

Is there a way for Hawking to organize the rounds such that he wins?

More info and solution “Rigging a Vote”
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Brain Teasers and Puzzles

Island of Blue Eyes

There is an island known for its people with blue eyes, yet there is at least one green-eyed person on the island. No one knows the color of their own eyes, as there are no reflective surfaces on the island and discussion of eye color is forbidden, but they can see everyone else’s eye color. If any islander were to come to know that they do not have blue eyes, they would leave the island in shame before the next sunrise.

One day, an outsider visits the island and remarked how there was at least one islander with green eyes. Within the day, every islander had heard and understood this new information.

Assuming departures from the island are noticed by everyone by the next day, and assuming each islander is highly logical and is able to keep track of all other islanders’ eye colors and actions – what happens to the islanders and does it depend on the number of green-eyed islanders?

This is a classic logic puzzle, also known under a different story (but same core logic) as Josephine’s Problem.

More info and solution “Island of Blue Eyes”
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Brain Teasers and Puzzles

Burning Ropes

You have two lengths of rope that take exactly 60 minutes to burn. The ropes burn unevenly so if you cut the rope in half, burning a half will not necessarily take 30 minutes.

How do you precisely measure 45 minutes using these two ropes?

More info and solution “Burning Ropes”
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Brain Teasers and Puzzles

Wrongly Labeled Boxes

You run a small business that sells and ships widgets. Today, you received three orders: one customer bought two blue widgets, one bought two red widgets, and one bought one red and one blue widget. Each widget is carefully packaged without any indication of the color inside, and then you pack the each order of two packaged widgets into boxes, tape them up, and stick shipping labels on them using your digital label printer.

However, there was a glitch with the software, and it labeled all three boxes incorrectly. You need to figure out the correct labels, but you forgot which box contained which widgets.

What is the fewest number of widgets you have to inspect before you know how to correctly label all the boxes, and which do you inspect?

This was a popular brainteaser in some engineering interviews a while back, often using “apples” and “oranges” instead of red and blue widgets.

Preparing for a brain teaser interview? Check out our ultimate guide to brain teaser interviews.

More info and solution “Wrongly Labeled Boxes”