Interview Brain Teasers

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

Impossible Sudoku

You may be familiar with Sudoku, a combinatorial number placement puzzle in which you fill in a 9×9 grid with digits such that each row, column, and 3×3 square contains all of the digits 1-9 exactly once.

You come across a Sudoku puzzle in which the initially populated numbers appear to be legal (no row, column, or square had the same number twice), but it is clear that trying to solve the puzzle would lead to an impossible arrangement of numbers – an unsolvable puzzle not because there is not enough information, but because it forces you into a contradictory/rule-breaking result. What is the smallest possible sum of the initial numbers?

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Pirate Survivor Puzzle

The democratic pirates are at it again! Since last time, they have become very successful and have now expanded to 100 pirates. They decide this is too large of a group for plundering, so true to their democratic roots, they want to settle it with a vote:

  1. They vote on whether to kick out the newest (least senior) pirate.
  2. If a majority votes “aye”, then the newest pirate is kicked out, and the process repeats with the remaining pirates.
  3. If half or more of the remaining pirates vote “nay”, then the vote is over and everyone remaining is safe.

Each pirate wants to stay in the group, but if that is assured, they would prefer to kick out as many other pirates as possible (fewer ways to split the treasure).

How many pirates will remain at the end of this process?

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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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