Brain Teasers and Puzzles

Favorite Fruit and Favorite Color

Ava, Beth, Cam, and Derek each have a different favorite fruit and favorite color. We know their favorite fruits are apple, banana, cherry, and durian, and their favorite colors are blue, green, red, and yellow. We also know:

  1. Cam does not like apples or cherries
  2. Derek’s favorite color is yellow and his favorite fruit is not banana
  3. The person whose favorite fruit is cherry also likes the color green
  4. Beth’s favorite color is red and her favorite fruit is not apple
  5. The person whose favorite fruit is durian does not like the color blue

What is each person’s favorite fruit and favorite color?

Brain Teasers and Puzzles

Color of the Last Ball

There is a bag with 20 blue balls and 13 red balls. Randomly remove 2 balls from the bag:

  • If they are the same color, replace them with a blue ball
  • If they are different colors, replace them with a red ball

Repeat this process until there is just 1 ball remaining. What is the color of the last ball?

Brain Teasers and Puzzles

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?

Brain Teasers and Puzzles

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. Not end up with the most candies, nor the fewest candies
  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?

Brain Teasers and Puzzles

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?

Brain Teasers and Puzzles

Lions and Sheep

On a magical island, there are 100 lions and 1 sheep, all of which can live by eating the plentiful grass on the island. Any lion that eats the sheep will magically turn into a sheep afterward, such that there will always be a sheep on the island.

Every lion would like to eat a sheep, but would much rather prefer to not be eaten (they wouldn’t mind turning into a sheep if they wouldn’t be eaten).

If all the lions act rationally and know all the other lions act rationally, how many lions will remain on the island in the end?

Brain Teasers and Puzzles

Number Deduction

A teacher gives three clever students in her class a challenge: she writes down 3 different numbers on 3 index cards, and has each student hold up one of the cards to their forehead such that they can’t see their own card but everyone else can.

She tells them each card has a different number, and that two of the numbers add up to the third number, and asks them to figure out their number without sharing the numbers they see.

Ava sees Sid has 40 on his forehead and Vlad has 60 on his forehead.

Ava says “I don’t know my number.”

Vlad says “I don’t know my number.”

Before Sid can say anything, Ava realizes she is now able to figure our her number! What is Ava’s number?

Brain Teasers and Puzzles

Fake Coins Proof

You are a rare coins expert and have determined there are 7 fake coins out of 14 gold coins. Now you need to prove to the judge which ones are fake.

It is known that that real coins all weigh the same, fake coins all weigh the same, and fake coins weigh less than real ones (but are otherwise identical).

Using a traditional double-pan balance scale just 3 times, can you prove exactly which of the 14 coins are fake?

Brain Teasers and Puzzles

Escape the Maze

In this maze of 8×8 rooms, each room has an arrow that points up, down, left, or right – and it will only let you move to the adjacent room in the direction of the arrow.

After you leave a room, or if you are unable to move because there is no adjacent room in the direction of the arrow (i.e., the arrow points outside the maze but there is no exit), the arrow in that room will rotate 90 degrees clockwise.

You start in the bottom left room, and the only exit is the right door in the top-right room.

Maze to escape from

Prove that no matter what the initial arrangement is, you will eventually escape the maze.

Brain Teasers and Puzzles

Four-Card Problem

You see four cards with A, D, 3, and 6 face-up. You know that each card has a letter on one side and a number on the other side.

You are told that cards with a vowel on one side must have an even number on the other side. Which cards do you need to turn over to test if this rule is broken?

Brain Teasers and Puzzles

3 Digit Code

You have six guesses to figure out a 3 digit code. After each guess, you will be told exactly how many digits are correct but in the wrong place and how many digits are correct and in the right place. You have made these five guesses already:

  • 865: exactly one digit in the right place
  • 964: exactly one correct digit but in the wrong place
  • 983: no correct digits
  • 548: exactly two correct digits but in the wrong places
  • 812: exactly one correct digit but in the wrong place

What is the correct 3 digit code?

Brain Teasers and Puzzles

Guess the Number

Jake has a 4-digit number in mind and asks Raj to guess the number. Raj can have 7 guesses, and Jake will give him some hints after 6 guesses.

Raj makes these 6 guesses:

  • 6 3 5 8
  • 9 3 0 6
  • 4 8 8 2
  • 6 7 2 8
  • 1 1 9 1
  • 5 6 2 7

These were all wrong, but Jake says every guess had exactly one (and only one) correct digit in the correct position. Additionally, all the digits are different.

What should Raj’s 7th guess be?

Brain Teasers and Puzzles

Last Chocolate Game

Two friends are playing a game with two boxes of chocolates. They take turns taking out some number of chocolates from the boxes, and whoever takes the last chocolate wins. Each turn they can take chocolates one of two ways:

  • Take any number of chocolates from a single box
  • Or take an equal number of chocolates from each box

If there are 25 chocolates in one box and 35 in the other, what is the winning strategy?

Brain Teasers and Puzzles

Who is Lying?

Amy says Brad is lying.
Brad says Chris is lying.
Chris says both Amy and Brad are lying.

Who is lying? Who is telling the truth?

Brain Teasers and Puzzles

Random Turns

You are in a city with streets on a perfect grid – every street is north-south or east-west. You are are driving north, and decide to randomly turn left or right with equal probability at the next 10 intersections.

After these 10 random turns, what is the probability you are still driving north?

Brain Teasers and Puzzles

Water Jug Riddle

You have a 3-litre jug and a 5-litre jug, and as much water as you need. How do you measure out exactly 4 litres using only these two jugs?

This is a classic logic puzzle, sometimes used in finance and engineering interviews many years ago. It also was featured in the movie Die Hard with a Vengeance!

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?

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?

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?

Brain Teasers and Puzzles

Logical List Puzzle

Which logical statement(s) below must be correct?

  1. Exactly one statement on this list is incorrect
  2. Exactly two statements on this list are incorrect
  3. Exactly three statements on this list are incorrect
  4. Exactly four statements on this list are incorrect
  5. Exactly five statements on this list are incorrect
  6. Exactly six statements on this list are incorrect
  7. Exactly seven statements on this list are incorrect
  8. Exactly eight statements on this list are incorrect
  9. Exactly nine statements on this list are incorrect
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?

Brain Teasers and Puzzles

Tennis Match Mystery

Abe, Ben, and Catelyn were playing 1-on-1 tennis matches one afternoon. After each match, the winner stayed on the court and the loser was replaced by the person who sat out.

At the end of their session, Abe had played 8 matches, Ben had played 12 matches, and Catelyn had played 14 matches. Ben was particularly exhausted as he had played all of the last 7 matches.

Is it possible to figure out who played and who won in the 4th match?

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?

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?

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.

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