Brain Teasers and Puzzles

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.

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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.

Difficulty - Medium, Number Theory

In some cultures, it is typical for guests at an event to shake hands when they meet other guests (when there isn’t a pandemic). Some might be more social and shake hands with a lot of other guests, while others may be less social and shake hands with few or no other guests.

Can you prove that, regardless of the number of guests at the event, there must be at least two guests with the same number of handshakes at the event? In other words, can you prove that it is impossible for every guest to have shaken a different number of hands?

Assume guests can’t shake hands with themselves.

Difficulty - Easy, Matchstick Puzzles, Simple Math

Matchstick Math 2

Move exactly 1 match 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 2 Chess Puzzle 2

White to play and mate in 2.

Difficulty - Medium, Word Puzzles

Middle Four Letters

The middle four letters of these 8-letter words are shown. Can you figure out the full 8-letter words? There may be multiple suitable answers for some of the words.

_ _ EQUA _ _
_ _ DUST _ _
_ _ CUBA _ _
_ _ COLA _ _
_ _ DIRE _ _
_ _ MESA _ _
_ _ TACO _ _
_ _ OPIC _ _

View Solution

Chess, Difficulty - Medium

How Many Ways to Mate?

How many ways can white mate in 1 move?

Difficulty - Medium, Geometry

Inscribed Squares

Above are two identical isosceles right triangles containing two inscribed squares.

In one, a perfect square has been inscribed such that two sides line up with the two legs of the right triangle. In the other, a perfect square has been inscribed such that one side lines up with the hypotenuse of the right triangle.

Is the inscribed square on the left larger or the one on the right?