# Brain teasers compilation

All credits to the creators of these brainteasers. I have simply compiled and classified them in order to prepare for interviews from a single webpage instead of clicking with fury all over the Internet. No open-ended answers (like the number of Turkeys sold for Thanksgiving) or trick questions (like the warm light bulb).

How to solve: decompose the problem, think about the probability of opposite event (for questions like what is the probability that at least one...).

Categories of brain teasers:

## Easy

scales

coins

cards

logic

computations

car speed problem

the cube faces

the clock

Bayesian conditional probabilities

**Using only a four-minute hourglass and a seven-minute hourglass, measure exactly nine minutes — without the process taking longer than nine minutes**

Start both hourglasses at 0 minutes. Flip over the four-minute glass when it runs out (at 4:00); ditto for the seven-minute glass (at 7:00). When the four-minute glass runs out the second time (at 8:00), the seven-minute glass will then have one minute of sand in its lower bulb. Flip the seven-minute glass over again and let the minute of sand run back. When the last grain falls, that will be nine minutes.

**You have a 3 litre jag and a 5 litre water jug. Jug does not have any marking. You have plenty of water or running tap. How would you measure 4 litres of water?**

Fill the 3-litter jug with water and pour into 5 litre jug

-5 litre jug contains 3 litres water.

Again, fill the 3-litter jug with water and pour into 5 litre jug (Now 5 litter Jug contains 5 litre water and 3 litre jug contains 1 litre water.

Empty 5 litre jug and pour 1 litre water from 3 litre jug (now, 5 litre jug contains 1 litre water)

Again, fill 3 litre jug and pour it into 5 litre jug (Now 5 litre jug contains 4 litre water)

**A book has N pages, numbered the usual way, from 1 to N. The total number of digits in the page numbers is 1,095. How many pages does the book have?**

Every page number has a digit in the units column. With N pages, that's N digits right there. All but the first 9 pages have a digit in the tens column. That's N - 9 more digits. All but the first 99 pages have a digit in the hundreds column (accounting for N - 99 more digits).I could go on, but not many books have more than 999 pages. A book with 1,095 digits in its page numbers won't, anyway.This means that 1,095 must equal: N + (N - 9) + (N - 99).This can be simplified to:1,095 = 3N - 108.That means that 3N = 1,203, or N = 401. That's the answer, 401 pages.

## Intermediate

- 100 balls into 2 boxes (1 and 99)
- back and forth question (bankers and bridge)
- the crash (solve for Yt = X - Zt)
- monty hall problem (3 doors and 1,000 doors)
- 1: Chess board, 8 by 8, how many squares in total?
- bacteria dividing by 2, when does it reach half (59min)
- guards door to freedom: what would the other guard say?

## Advanced

slot machines problem

plane passenger problem (proba 1/2)

#### There are 10 slot machines in front of me. In 9 of them the coins weigh 10g, in one of them the coins weigh 20g. You can take as many coins as you like out of each machine. How do you find the machine with the heaviest coins in one weighing?

Answer: Put 1 coin from machine 1, 2 coins from machine 2, 3 coins from machine 3 on the scale… If F is the final weight, then the difference between F is (1+2+3+…+10) allows you to find the machine with the heaviest parts. Indeed (F-(1+2+…+10))/20 gives us the number of this machine, so the number of the machine is (F-55)/20. That solution is super smart so congrats if you found it by yourself.

**Using only a four-minute hourglass and a seven-minute hourglass, measure exactly nine minutes—without the process taking longer than nine minutes.**

#### What is the angle between the hour-hand and minute-hand of a clock at 3:15?

7.5 degrees

References:

- https://reworking.com/15-brain-teaser-interview-questions-and-answers/
- http://sellsidehandbook.com/interview/brain-teasers/
- https://365financialanalyst.com/career-advice/answering-tips-for-brainteaser-interview-questions/
- https://www.simtrade.fr/blog_simtrade/classic-brain-teasers-real-life-interviews/
- https://en.wikipedia.org/wiki/Monty_Hall_problem
- https://www.wallstreetoasis.com/forum/investment-banking/brain-teasers-examples
- https://archive.is/L89UO#selection-4347.0-4347.149