Brain Teasers and Puzzles

Brain teasers, puzzles, riddles, and other challenges

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?

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7 Actual Brain Teaser Interview Questions and Answers

Brain teaser interview questions were quite common in tech, finance, and consulting interviews for a period of time. Here are 7 brain teaser interview questions and answers encountered in actual interviews, including engineering interviews at Apple and Microsoft – how many can you solve?

If you want to learn more about brain teaser interviews, check out our guide to brain teaser interview questions.

1. Incorrectly Labeled Boxes (easy)

Asked in a software quality assurance engineer interview at Apple.

There are three boxes: one with only apples, one with only oranges, and one with both apples and oranges. All three boxes are incorrectly labeled (e.g., the “apples” label is on either the “apples+oranges” box or the “oranges” box). Is there a way to figure out the correct labels for all three boxes if you are only allowed to see one fruit from one of the boxes?

Solution to #1

If you see one fruit from the box labeled “apples+oranges”, then you know for sure that box contains only that fruit, because it cannot be the “apples+oranges” box as all boxes are labeled incorrectly.

Let’s say you saw an apple from the box labeled “apples+oranges”. That box must be the “apples” box. Then the box labeled “oranges” must contain apples and oranges, because it cannot be the “oranges” box (all boxes are labeled incorrectly) and the “apples” box has already been found. Then the remaining box labeled “apples” must be the “oranges” box.

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Password to Exclusive Club

A man wants to enter an exclusive club, but doesn’t know the password. He observes a few other patrons:

  • First patron walks up and the doorman just says “12”. The patron replies “6” and is let in.
  • Second patron walks up and the doorman says “6”. The patron replies “3” and is let in.

Thinking he has figured it out, the man walks up and the doorman says “10”. The man replies “5” but it’s incorrect and he is turned away.

What should the man have said instead?

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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.

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Same Number of Handshakes

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.

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