Difficulty – Medium

Medium difficulty brain teasers and puzzles

Difficulty - Medium, Interview Brain Teasers, Number Theory

Moving Battleship Puzzle

You are trying to hit a moving battleship, but you have no way of monitoring its position. However, you have the following information:

You know where the battleship started.
You know when the battleship started moving.
You know the battleship is only moving along a straight line.
You know the battleship moves a constant speed per hour, and that speed is an integer. But you do not know what that speed is.

Every hour, you can fire precisely once at any point on that line. Is there a strategy you can use that will guarantee you will hit the battleship in a finite amount of time?

Fun fact, this was an actual brainteaser given to me in the second 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 - Medium, Word Puzzles

One Acts Kind at the Spa

Which English word can be added to either the beginning or end of each of the following words, in order to create four valid English words?

ONE
ACT
KIND
SPA

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

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?