Difficulty – Medium

Medium difficulty brain teasers and puzzles

Difficulty - Medium, Interview Brain Teasers, Logic Puzzles, Number Theory

Deducing Bicycle Spokes

A bicycle shop has some number of unusual bicycles. All their bikes are identical (there’s more than one bike), and each bike’s front and back wheels has at least one spoke each (each bike has more than one spoke). 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?

Chess, Difficulty - Medium

Bishop Wins the Day

White to play and mate in two moves.

Difficulty - Medium, Matchstick Puzzles, Simple Math

Match Maximization

What is the biggest number you can make by moving exactly 2 matches in the number above?

Assume that numbers must be represented in their standard “digital clock” font (for example, a “1” requires two segments).

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 - 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 - Medium, Interview Brain Teasers, Probability

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.

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 - 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?