Brain Teasers and Puzzles

Brain teasers, puzzles, riddles, and other challenges

Difficulty - Hard, Interview Brain Teasers, Probability

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?

Difficulty - Easy, Riddles and Lateral Thinking

Solitary Word

I am a solitary word.

If I lose my first letter, I remain the same.

If I lose my first letter again, I still remain the same.

What am I?

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Difficulty - Very Easy, Riddles and Lateral Thinking

Sword is Mightier than the Bow

Shot two arrows at its center and missed both times,
swung a sword once at its center and hit twice.
What is it?

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Difficulty - Very Easy, Simple Math

Swap Digits

Swap two of the digits in this equation to make it a valid equation:

7 x 7 + 9 x 9 = 138

Difficulty - Medium, Game Theory and Game Strategies

Card Pairing Game

You are playing a game with your friend using a standard deck of 52 playing cards. Each round, you flip over two cards:

If both cards are black, you keep the cards and earn one point.
If both cards are red, your friend keeps the cards and earns one point.
If one card is red and one is black, the cards are set aside in a discard pile.

What is the probability that you end up with more points than your friend when all the cards in the deck have been used up?

Difficulty - Medium, Geometry

Square in a Square

In the larger square, there is a smaller square formed by lines connecting each corner to the midpoint of one of the sides.

Question: What fraction of the larger square is the smaller filled square?

Difficulty - Easy, Rebus

Rebus Puzzle 1

What common word or phrase is this rebus referring to?

 T  M  C
 A  U  O
 H  S  M
 W  T  E

Solution

What goes up must come down

Difficulty - Medium, Patterns, Sequences, and Sets

Nob’s Number Tree Puzzle

Nob’s Number Tree

What number belongs in the “?” circle? Note that all numbers shown are correct, there are no typos or errors.

Nob Yoshigahara’s Puzzles

Nob’s Number Tree is a well-known brainteaser by the Japanese puzzle guru Nobuyuki “Nob” Yoshigahara, who wrote many mathematical puzzle books and invented many puzzle toys. This cheeky number tree puzzle seems straightforward, but the straightforward solution falls apart when you arrive at the bottom.

Difficulty - Easy, Riddles and Lateral Thinking, Simple Math

Missing Dollar Riddle

The missing dollar riddle is a classic brain teaser that can trip up even savvy puzzle solvers:

Three friends split the cost of a hotel room. They are charged $30, so each of them pays $10.

Later the hotel manager realized the room only cost $25 instead of $30. The manager brings $5 to reimburse the friends.

The manager finds it hard to split $5 three ways, so he gives the friends $1 each, and keeps $2 for himself.

But wait – each friend paid $9, for a total of $27, and the manager pocketed $2. That’s 27 + 2 = 29, whereas they originally handed over $30. Where did the missing dollar go?

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Difficulty - Hard, Number Theory

Divisible by 100

Prove that for any set of one hundred whole numbers, either one of those numbers is divisible by 100 or the sum of a subset of those numbers is divisible by 100.