Difficulty – Medium

Medium difficulty brain teasers and puzzles

Algebra, Difficulty - Medium

Ferry Boat Problem

Two ferry boats serve the same route on a river, but travel at different speeds. They depart from opposite ends of the river at the same time, meeting at a point 720 yards from the nearest shore.

When each boat reaches the other side, it takes 10 minutes to unload and load passengers, then begins the return trip. This time, the boats meet at a point 400 yards from the other shore.

How wide is the river?

The ferry boat problem is created by well-known puzzle author Sam Loyd.

Algebra, Difficulty - Medium

Sum of Powers

Find a combination of three different positive integers x, y, and z such that:

x³ + y³ = z⁴

Hint: there’s a better way than brute force / trial & error.

Difficulty - Medium, Word Puzzles

These Wordle puzzles are nearly complete, you just need to finish them by figuring out the correct word. In each of these 5 puzzles, there should be just one or two valid answers remaining – find them!

Haven’t played Wordle before? You get 6 tries to guess the 5-letter English word, and for each guess you are shown whether each letter is in the right place in the word (green), in the word but in the wrong place (yellow), or not in the word at all (gray).

View Solution

Difficulty - Medium, Interview Brain Teasers, Probability

Russian Roulette Riddle

In the morbid game of Russian Roulette, a partially loaded revolver with a six-chamber cylinder is randomly spun, pointed at one of the players, and fired. If the revolver landed on an empty chamber, the lucky player is safe, and the process is repeated with the next player. The obvious objective of the game is to not get shot.

You find yourself stuck in a game of Russian Roulette. A freshly loaded revolver is aimed at the first player, and it turns out to be an empty chamber. Your turn is next, and you are given the choice to either:

Spin the cylinder before pulling the trigger (i.e., you get a random new chamber)
Or just pull the trigger (i.e., let the revolver fire whatever is in the next chamber)

Which choice should you pick if the revolver was originally:

Loaded with one bullet?
Loaded with bullets in two random chambers?
Loaded with bullets in two consecutive chambers?

Assume the revolver cannot misfire, and that spinning the cylinder lands on all chambers with equal probability.

Some variation of this Russian Roulette riddle was once asked in interviews at Jane Street, Susquehanna International Group (SIG), Facebook (now Meta), UBS, Capital One, and more.

Difficulty - Medium, Word Puzzles

Vocabulary Puzzle

Quick vocabulary puzzle – given the middle four letters of each word, figure out these 8-letter words:

_ _ TABA _ _
_ _ CUME _ _
_ _ NERO _ _
_ _ IDEN _ _
_ _ NETA _ _
_ _ EASA _ _
_ _ ENAR _ _
_ _ WERF _ _

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Difficulty - Medium, Matchstick Puzzles, Simple Math

Matchstick Math 3

Rearrange exactly 2 matches to make this a valid equation.

In matchstick math puzzles, you are not allowed to make an inequality symbol such as ≠, ≥, >, <, or ≤. That would make it too easy!

Chess, Difficulty - Medium

Mate in 3 Chess Puzzle 1

White to play and mate in 3.

Difficulty - Medium, Interview Brain Teasers, Number Theory, Simple Math

I Like the Numbers 4 and 5

I like the numbers 4 and 5. I like to add 4’s and 5’s together to make other numbers, such as 4 + 4 + 5 + 5 + 5 = 23. How many numbers from 1 to 1000 can be written as the sum of 4’s and 5’s?

Difficulty - Medium, Interview Brain Teasers, Logic Puzzles

Lions and Sheep

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?

View Solution

Difficulty - Medium, Interview Brain Teasers, Physics and Science

Throwing Rocks Off a Boat

A man is throwing rocks off a boat floating in the middle of a lake. The rocks sink quickly to the bottom of the lake.

Does the water level in the lake rise, fall, or stay the same after the rocks are thrown off the boat and sink to the bottom of the lake?

This question was asked in an actual mechanical engineering interview.

Preparing for a brain teaser interview? Check out our ultimate guide to brain teaser interviews.

Hint

Consider Archimedes’ principle and how the rocks affect the water level while they are on the boat vs. how the rocks affect the water level when they are in the lake.