Brain Teasers and Puzzles

Brain teasers, puzzles, riddles, and other challenges

Difficulty - Medium, Interview Brain Teasers

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?

Difficulty - Easy, Word Puzzles

Complete the Words

P _ _ _ N T
D E _ _ _ ST
S T _ _ _
C _ _ _ E R

Which 3-letter word can be inserted into all four lines above to form complete words?

Chess, Difficulty - Hard

Take Back a Move Chess Puzzle

This creative Leonid Kubbel chess puzzle has white take back a move and then checkmate!

White just made a move, but then realized there was a mate in 1 on the last move and missed it. What was white’s last move, and what was the mate in 1?

Difficulty - Easy, Interview Brain Teasers, Number Theory

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.

Difficulty - Very Easy, Interview Brain Teasers

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?

Difficulty - Hard, Patterns, Sequences, and Sets, Word Puzzles

Cryptic Pattern Puzzle

Replace the ?’s in each of these to complete the puzzle:

Part 1

“Asia” is H
“Cuffs” is S
“Ender” is I
“Redness” is F
“Fuchsia” is ?

Part 2

“Using” is E
“Desist” is I
“Visits” is E
“Design” is ?

Part 3

“Gross” is W or R
“Assign” is S
“Amassing” is E
“Design” is S
“Amassing” is S
“Arrows” is ? or ?

Part 4

“Pro-tem” and “row” are H
“Ties” is K
“Cohesion” is A
“Casino” is E
“Hocks” is either a word, name, ? or ?

Part 5

“Edna” is I
“Slang” is X
“Siege” is E
“Basin” is X
“Sin” is X
“Sin” is A
“Besiege” is X
“Signals” is ? and ?

Source: Matt Malone on Puzzling StackExchange (spoiler warning: contains the solution)

Difficulty - Easy, Game Theory and Game Strategies, Interview Brain Teasers, Logic 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?

Difficulty - Hard, Interview Brain Teasers, Logic 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.

Difficulty - Medium, Geometry

Five’s a Crowd

Try to place five points in (or on the perimeter of) an equilateral triangle with side length 10, as to maximize the distance between the points.

What is the greatest possible distance between the two closest points?

Difficulty - Medium, Interview Brain Teasers, Physics and Science

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?