Tag Interview Brain Teasers

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

Majority Vote Puzzle

After the results of an election, you are told that one candidate has received the majority of the votes, but you don’t know which candidate. You have exactly one opportunity to hear the votes, but:

  • The list of votes is very long
  • The votes will be announced one after another in random order
  • You have a poor memory (can only remember a couple of names or numbers)
  • You are not allowed to write or record anything

Given these restrictions, is there a way figure out which candidate received the majority of votes?

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Tale of Two Trains

There are two trains that run between two cities. The trains are identical and run on identical routes, so passengers have no preference between the two and would take whichever train that pulls into the station. The trains run at the same frequency: exactly once an hour.

You often travel between the two cities on a whim, and when you do so, you show up at the station at a completely random time. Yet after many trips over the years, you notice that you have taken one of the trains three times as often as the other. Is this just really bad/good luck, or is there another likely explanation?

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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.

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Deducing Bicycle Spokes

A bicycle shop has some unique bicycles. Each bike is identical, and each bike’s front and back wheels has at least one spoke each. 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?

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