Interview Brain Teasers

Brain teasers you might encounter in a finance, consulting, or engineering interview

Flipping Every N-th

There are 100 face-down cards. The first person that passes by flips over every card, the 2nd person that passes by flips over every 2nd card, and so forth – the n-th person that passes by flips over every n-th card. Before you know it, 100 people have passed by.

After all 100 people have passed by, which cards are face-up and which are face-down?

Fun fact, this was an actual brainteaser given to me in the first round interview for a hedge fund internship back in 2011.

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Rigging a Vote

There are five candidates participating in an unusual election. There are four rounds of voting, and only two candidates participate in each round, with the winner moving on and the loser dropping out. This means first candidate 1 will run against candidate 2, then the winner will run against candidate 3, and so on, with the winner of the last round being elected.

Polling shows that Stephen Hawking is not very popular. There are five equal-sized groups in the voting population, and polling shows they prefer the candidates in the following order:

  • Group 1: Einstein > Newton > Maxwell > Hawking > Curie
  • Group 2: Newton > Curie > Maxwell > Einstein > Hawking
  • Group 3: Curie > Maxwell > Einstein > Newton > Hawking
  • Group 4: Einstein > Newton > Hawking > Curie > Maxwell
  • Group 5: Newton > Maxwell > Einstein > Hawking > Curie

But Hawking has a secret weapon – he gets to choose the order the candidates participate in each round.

Is there a way for Hawking to organize the rounds such that he wins?

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Island of Blue Eyes

There is an island known for its people with blue eyes, yet there is at least one green-eyed person on the island. No one knows the color of their own eyes, as there are no reflective surfaces on the island and discussion of eye color is forbidden, but they can see everyone else’s eye color. If any islander were to come to know that they do not have blue eyes, they would leave the island in shame before the next sunrise.

One day, an outsider visits the island and remarked how there was at least one islander with green eyes. Within the day, every islander had heard and understood this new information.

Assuming departures from the island are noticed by everyone by the next day, and assuming each islander is highly logical and is able to keep track of all other islanders’ eye colors and actions – what happens to the islanders and does it depend on the number of green-eyed islanders?

This is a classic logic puzzle, also known under a different story (but same core logic) as Josephine’s Problem.

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Boxes of Apples and Oranges

There are three identical boxes of apples and oranges, except one contains all apples, one contains all oranges, and one contains a mix.

The boxes are labeled “apples”, “oranges”, and “apples and oranges” but all 3 boxes were labeled incorrectly!

You have the opportunity to inspect fruit from the boxes one at a time, without looking inside the box. What is the fewest number of fruit you need to inspect to correctly label the contents of the identical boxes?

This was a popular brainteaser in some engineering interviews a while back, including a software quality assurance engineer interview at Apple.

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