Brain Teasers

Brain teasers are an important part of the trading interviews. There is almost no trading firm that won’t ask you to solve a brain teaser or a puzzle. Your approach and behaviour during solving might become more important than the actual answer itself. 

What is important during the interview?

Ask enough questions, listen well to the information that is provided and don’t stress out due to the interview setting. Also, the interviewer will provide you with some hints – when you don’t work the solution out right away. It is important that you listen carefully to these hints, as these should make you capable to solve the final solution.

How to prepare

Trading Interview provides you with a wide variety of brain teasers that are on an interview level. Try to solve them by yourself. If you do not know the answer, press ‘Hint’ instead of looking at the answer. Also, try to interview your friends with these kind of brain teasers. It is good to experience how a brain teaser is experienced from ‘the other side of the table’. Try to lead your friend with some hints to the final solution. Here you can try out a few example brain teasers.

What kind of brain teasers are there?

Brain teasers come with different variations. The brain teasers on this website will be labeled to indicate which variant you are practising. The provided brain teasers contain the  following variations:

• (Logical) Apply a logical reasoning – As with most brain teasers, problems with logical reasoning usually do not contain hard math. Most of the time there is not even a single step in solving that contains any math. It is mostly a matter of ‘if this, then that, and if this, then that’. However, recognising the solution is usually harder than some tough math question. 
• (Simplification) Start with a simplification – Some brain teasers require to be simplified. Start with a small amount of the problem, what happens when the problems becomes larger from this starting point? 
• (Out of the Box) Thinking out of the box –  These are usually the harder ones. Most part of the puzzle seems ‘too easy’, but you just couldn’t finish the final part of the puzzle. Why, is there something wrong with the puzzle? No, try to think out of the box and see how you can solve the puzzle!
• (Symmetry) Solving the symmetry – Some brain teasers require you to recognise a symmetry in the problem. After recognising the symmetry, the problem becomes way easier to solve!
• (Summation) Recognising serial summations – These are the type of brain teasers that involve some math. Sometimes it might be good to have a basic knowledge of math tricks, like a summation of numbers. There is an easy way of summing up all the numbers from one to N. Take for example the first five numbers. Write the serie of numbers out from one to five and do the same from five to one:
  
  

  1, 2, 3, 4, 5
  5, 4, 3, 2, 1

  If we sum the numbers vertically, we get:

  6, 6, 6, 6, 6.

  So now we have five times the number six. Summing all these sixes results in 30, which is the summation of two times the series one to five. Therefore, the actual value of the summation of one to five is equal to:

  5*6/2 

  This leads us to a general formula for the summation of the numbers one to N:

  N(N+1)/2 

  This trick will help you to solve some of the problems.

• (Modular) Recognising modular arithmetic – To understand these types of problems, you have to understand the modulo operator. The modulo operation is denoted as X mod Y, which finds the remainder of the division of the number X by Y. For example, 11 mod 3 would be equal to 2, because 11/3 = 3.67. This number has to be rounded down to 3, so we have 11 – 3*3 = 2.
• (Pigeon Hole) The Pigeon Hole principle – This is a well known principle in which there are more pigeons than there are holes. So, if we would start filling all the pigeon holes, there would be at least one hole that is filled with more than one pigeon. It would surprise you how many problems can be solved by this simple principle! An example is: You have ten red socks and twenty blue socks. How many socks do you need to take out of your closet before you know for sure that you have a matching pair? We have two holes, namely both colours. We need three pigeons (socks) before we know for sure that at least one hole has two or more pigeons. In other words: we need three socks.