## Problem Definition

### Number sequence

**Situation:**

“You and I will take turns saying numbers. The first person will say a number between 1 and 10. Then, the other person will say a number that is greater than the first number. The difference between both numbers must be between 1 and 10. We will keep going back and forth in this way until one of us says the number 50. That person wins. You will start.”

**Question:**

What number should you start with?

### U2 Concert

**Situation: **

U2 has a concert that starts in just 17 minutes. To get there, all the band members must cross a bridge. Since the bridge is old, a maximum of two people can cross the bridge at any one time. To make matters worse, it is dark and there is only one torch. Anyone crossing the bridge must carry a torch. The torch cannot be thrown across the bridge. Instead, someone must walk it back to the other side. Each band member walks at a different speed. If two members cross at the same time, both must walk at the speed of the slower band member.

- Bono takes 1 minute to cross.
- Edge takes 2 minutes to cross.
- Adam takes 5 minutes to cross.
- Larry takes 10 minutes to cross.

**Question:**

Can the band make it to the concert in time? How will they manage this?

### Buckets

**Situation:**

You have a 5-gallon bucket and a 3-gallon bucket. (Assume that you have an unlimited supply of water and that the buckets do not have any markings for measurement.

**Question:**

How can you get 4 gallons of water into the 5-gallon bucket?

### Cigars

**Situation:**

A homeless man collects cigar butts. He uses 5 cigar butts to make a new cigar. Today, he has collected 25 cigar butts.

**Question:**

How many cigars can he smoke?

## Comments

Brain teasers are short but difficult questions. They test your analytical skills and your ability to think outside the box. They also show the interviewer your ability to elaborate on difficult real-world tasks. The interviewee should solve each brain teaser in about 5-10 minutes.

If the interviewee gets stuck (i.e. spends more than 10 minutes), suggest that the interviewee should proceed to the next brain teaser.

## Short Solution

## Detailed Solution

### Number Series

You should start with 6. To win the game, you should say the following sequence of numbers: 17, 28, 39, 50.

- Since you want to say 50 first, you need to make the other person say a number between 40 and 49.
- Thus, you should say 39.
- If you want to say 39, you need to make the other person say a number between 29 and 38.
- Therefore, you should say 28.

According to this logic, you will say 17 before 28. Thus, to win, you should start the game with 6.

### U2 Concert

- Bono and Edge cross - 2 minutes.
- Bono returns - 1 minute.
- Adam and Larry cross - 10 minutes.
- Edge returns - 2 minutes.
- Bono and Edge cross - 2 minutes.

Total - 17 minutes

### Buckets

- Fill the 3-gallon bucket and empty it into the 5-gallon bucket
- Fill the 3-gallon bucket and empty it into the 5-gallon bucket again. This leaves 1 gallon in the 3-gallon bucket
- Empty the 5-gallon bucket
- Pour the gallon in the 3-gallon bucket into the 5-gallon bucket
- Fill the 3-gallon bucket and empty it into the 5-gallon bucket again

You have with 4 gallons of water in the 5-gallon bucket.

### Cigars

He can make 6 cigars. 25 cigarette butts will make 5 cigars. After the man has smoked all 5 cigars, he has 5 cigarette butts left to make a 6th cigar.

## Difficult Questions