Case

# Brain Teasers - Motel

Solved 2.2k times
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

## Problem Definition

### Motel

Situation:
Three friends check into a motel for the night. The clerk tells them the bill is \$30, payable in advance. They each pay the clerk \$10 and go to their room. A few minutes later, the clerk realizes he has made an error and overcharged the trio by \$5. He asks the bellhop to return \$5 to the 3 friends who had just checked in. The bellhop sees this as an opportunity to make \$2 as he reasons that the three friends would have a tough time dividing \$5 evenly among them; so he decides to tell them that the clerk made a mistake of only \$3, giving a dollar back to each of the friends. He pockets the leftover \$2 and goes home for the day!

Question:
Now, each of the three friends gets a dollar back, thus they each paid \$9 for the room which is a total of \$27 for the night. We know the bellhop pocketed \$2 and adding that to the \$27, you get \$29, not \$30 that was originally spent. Where did the other dollar go?

### Murder

Situation:

The midnight train is coming down the mountains. Art Farnanski seems to be sleeping in his seat. At the station, all the passengers get off the train except one. The conductor comes and taps him on the shoulder to let him know they have arrived. Art Farnanski does not answer. He is dead.
Hours later the four people that had shared the train compartment with the dead man are at the police station.
The man in the dark suit:
"I'm innocent. The blonde woman was talking to Farnanski."
The blonde woman:
"I'm innocent. I did not speak to Farnanski."
The man in the light suit:
"I'm innocent. The brunette woman killed him."
The brunette woman:
"I'm innocent. One of the men killed him."

Question:
The police detective comes up to you and says: “I know that four statements are wrong and four are true. Who killed Farnanski? (Only one person is guilty).”

### Trees

Statement:
You have 10 trees and you have to plant them in five rows, but each row must contain 4 trees.

Question:
How is this possible?

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

### Motel

The facts in this riddle are clear: There is an initial \$30 charge. It should have been \$25, so \$5 must be returned and accounted for. \$3 is given to the 3 friends, \$2 is kept by the bellhop - there you have the \$5. The trick to this riddle is that the addition and subtraction are done at the wrong times to misdirect your thinking - and quite successfully for most.

Each of the 3 friends did indeed pay \$9, not \$10, and as far as the friends are concerned, they paid \$27 for the night. But we know that the clerk will tell us that they were charged only \$25. The additional \$2 is kept by the bellhop. When you add the \$3 returned with the \$2 kept by the bellhop, you come up with \$30.

### Murder

The blonde woman killed Mr Farnanski.

There are only four true statements. Only one is guilty. Therefore, three of the "I'm innocent" statements are true. Only one more statement can be true.

If you compare the statements, the statement by the man in the dark suit or by the blonde woman must be correct. Therefore, "The brunette killed him" and "One of the men killed him" are false statements, so the blonde woman is left.

### Trees

Plant the trees in shape of a star:

## Difficult Questions

Related consulting question(s)

Hi Anonymous, there may be several reasons for that; some of them, in order of frequency, are: Your structure is not complete enough – you are just using not MECE/ not complete structure... (more)

Hey, I am new to this too, but I think I have some ideas for your problem. Your approach looks good, but I think you have a mistake in how you time the trains. You say that there is one train ev... (more)

Hi, good question! Probably somewhat depending on your interviewer, but this is my view on it. In this situationit's important to try to showcase as mluch of your consulting skills as possible. Be t... (more)

Hi, here's how I would approach it - Define the geographic area to be covered [the whole world? the U.S.? NYC? Manhattan?...for this example I'll use Manhattan] - Population living there [~ 1... (more)

Hi, First of all, I totally agree with Francesco on the process. You should always come back to the cases you've solved and reevaluate your structures. Secondly, I believe it's very much related... (more)

Related BootCamp article(s)

## 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.

4 Comment(s)

## Brain Teasers

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

2 Comment(s)
4.7 (287 ratings)
Case exhibits

No case exhibits yet