Brain EaserClassic logic puzzles in which you infer or deduce actions and outcomes based on information provided
There is a bag with 20 blue balls and 13 red balls. Randomly remove 2 balls from the bag:
Repeat this process until there is just 1 ball remaining. What is the color of the last ball?
A prison warden was feeling capricious and played a game with the prison keys:
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?
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):
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?
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:
Can you figure out x and y using this information?
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?
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?
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?
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.
Prove that no matter what the initial arrangement is, you will eventually escape the maze.
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?
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:
What is the correct 3 digit code?
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:
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?
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:
If there are 25 chocolates in one box and 35 in the other, what is the winning strategy?
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?
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?
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!
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?
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:
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?
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?
Which logical statement(s) below must be correct?
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:
Given these restrictions, is there a way figure out which candidate received the majority of votes?
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?
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?
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?
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:
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.
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:
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?