Interview Brain Teasers

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

Number Deduction

A teacher gives three clever students in her class a challenge: she writes down 3 different numbers on 3 index cards, and has each student hold up one of the cards to their forehead such that they can’t see their own card but everyone else can.

She tells them each card has a different number, and that two of the numbers add up to the third number, and asks them to figure out their number without sharing the numbers they see.

Ava sees Sid has 40 on his forehead and Vlad has 60 on his forehead.

Ava says “I don’t know my number.”

Vlad says “I don’t know my number.”

Before Sid can say anything, Ava realizes she is now able to figure our her number! What is Ava’s number?

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Fake Coins Proof

You are a rare coins expert and have determined there are 7 fake coins out of 14 gold coins. Now you need to prove to the judge which ones are fake.

It is known that that real coins all weigh the same, fake coins all weigh the same, and fake coins weigh less than real ones (but are otherwise identical).

Using a traditional double-pan balance scale just 3 times, can you prove exactly which of the 14 coins are fake?

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3 Digit Code

You have six guesses to figure out a 3 digit code. After each guess, you will be told exactly how many digits are correct but in the wrong place and how many digits are correct and in the right place. You have made these five guesses already:

  • 865: exactly one digit in the right place
  • 964: exactly one correct digit but in the wrong place
  • 983: no correct digits
  • 548: exactly two correct digits but in the wrong places
  • 812: exactly one correct digit but in the wrong place

What is the correct 3 digit code?

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Guess the Number

Jake has a 4-digit number in mind and asks Raj to guess the number. Raj can have 7 guesses, and Jake will give him some hints after 6 guesses.

Raj makes these 6 guesses:

  • 6 3 5 8
  • 9 3 0 6
  • 4 8 8 2
  • 6 7 2 8
  • 1 1 9 1
  • 5 6 2 7

These were all wrong, but Jake says every guess had exactly one (and only one) correct digit in the correct position. Additionally, all the digits are different.

What should Raj’s 7th guess be?

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Ants on a Stick

Six ants are walking at 1cm/second on a very narrow stick 100cm long:

  • Ant 1: starts at 0, facing right
  • Ant 2: starts at 20, facing right
  • Ant 3: starts at 30, facing left
  • Ant 4: starts at 40, facing right
  • Ant 5: starts at 60, facing right
  • Ant 6: starts at 80, facing left
Ants on a Stick

When two ants run into each other, they immediately turn around and walk in the other direction.

How long does it take before the last ant walks off the stick?

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Confusing Zip Codes

The U.S. uses 5-digit zip codes to help determine where mail goes. Since mail can be oriented in all sorts of directions, they avoid assigning zip codes that could be confused with a different zip code when read upside-down. For example, 61666 could be confused with 99919 when upside-down, so mail could be accidentally routed to the wrong zip code if both were actual zip codes.

How many zip codes could be confused with a different zip code when read upside-down?

In the example above, 61666 and 99919 would count as two confusing zip codes. Also, zip codes are allowed to start with 0, such as 00501.

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