Case

# Brain Teasers - Light Bulb

Solved 2.0k times
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

## Problem Definition

### Light Bulb

Situation:

You are standing in front of a room with one light bulb inside of it. You cannot see if it is on or off. Outside the room there are 3 switches in the off positions. You may turn the switches any way you want to. You can open the door and enter the room, but you cannot use a switch anymore afterwards

Question:

How can you determine which switch turns the light on and off?

### Coins

Situation:

You have a pile of 24 coins. Twenty-three of these coins have the same weight, and one is heavier. Your task is to determine which coin is heavier and do so in the minimum number of weighings. You are given a beam balance (scale), which will compare the weight of any two sets of coins out of the total set of 24 coins.

Question:

How many weighings are required to identify the heavier coin?

### Truth or Lie

Situation:

You are in a room with 2 doors leading out. Behind 1 door is a coffer overflowing with jewels and gold, along with an exit. Behind the other door is an enormous, hungry lion that will eat anyone opening the door.

You do not know which door leads to the treasure and exit, and which door leads to the lion. In the room you are in with 2 men. The first is a knight, who always tells the truth, and a knave, who always lies. Both of these individuals know what is behind each door. You do not know which individual is the knight, or which one is the knave.

Question:

You may ask one of the individuals exactly 1 question. What should you ask in order to be certain that you will open the door with the coffer behind it, instead of the hungry lion?

### Dogs

Situation:

Two scruffy dogs were walking down the street. The first dog turned to the other and said, "Do you realize that if one of your fleas jumped onto me we would have the same number of fleas?" The second replied, "Yes, but if one of your fleas jumped onto me I would have five times as many fleas as you."

Question:

How many fleas are on each dog to begin with?

Brain Teasers are short questions with difficult logical or creative answers. They are a good way to test your analytical skills and capacity to think out of the box. These short questions also show the interviewer your ability to elaborate on difficult tasks from the real world. Each Brain Teaser is supposed to be solved by the interviewee in about 5-10 minutes.

If the interviewee gets stuck in a brain teaser (i.e. spends more than 10 minutes), propose to go on to the next one.

## Detailed Solution

### Light bulb

You turn 2 switches "on" and leave 1 switch "off" and wait about a minute. Then enter the room, but just before you enter, turn one switch from "on" to "off". Once in the room, feel the light bulb - if it is warm, but off, it has to be the last switch you turned off. If it is on, it has to be the switch left on. If it is cold and is off, it has to be the switch you left in the off position.

### Coins

It can be done in three weighings.

• Weighing 1: Break the coins into three piles of eight. Weigh one group of eight against another group of eight. If the scale balances, then the group that hasn't been weighed has the heavier coin. If the scale tips, then that group contains the heavier coin.
• Weighing 2: Break the group of eight that has the heavier coin into three groups (three coins, three coins, and two coins). Weigh one set of three against the other set of three. If it balances, the group of two has the heavier coin. If the scale tips, then that group has the heavier coin.
• Weighing 3: If the heavier coin is in the group of two, then just weigh one coin against the other to determine the heaviest coin. If the heavier coin is in a group of three, then take two of those coins and weigh them against each other. If the scale balances, the coin that hasn't been weighed is the heavier coin. If the scale tips, then that is the heavier coin.

### Truth or Lie

You ask one of the individuals what the other one would say if you asked him which door is holding back the hungry lion and then open this door.

### Dogs

One dog has two flees, the other dog has four.

## Difficult Questions

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## Brain Teasers

Learn how to tackle brain teasers and what purpose they serve in consulting case interviews

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## Typical Question Types in Written Tests

Questions among all tests can be categorized in math, GMAT-style, chart reading and brain teaser questions. Each type needs to be approached differently.

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