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Example Math Puzzles

Quant-trading-level problems that test mathematical reasoning and problem-solving — with full worked solutions.

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These are the math puzzles you meet at quant-trading interviews — problems that test how you reason mathematically and break things down, rather than how fast you can do arithmetic. The examples below sit at the difficulty these interviews tend to ask.

If you are after raw arithmetic speed or number sequences, those live in our separate mental math and sequences course; this page is about the harder, less mechanical problems.

Sample Questions & Solutions

Each question is a real interview problem. Try it yourself first, the full solution is revealed below.

Q1

Number of Pigs

Easy
You walk into a barn and see a collection of pigs (P), chickens (C) and horses (H). You notice that there are 480 legs in total.
  • The number of chickens is twice the number of horses.
  • The number of pigs is twice the number of chickens.
Compute the number of pigs.
Show solution
The provided info is:
  • The number of chickens (C) is twice the number of horses (H).
  • The number of pigs (P) is twice the number of chickens.
  • There are 480 legs in total.
So, \begin{equation} C = 2H \end{equation} \begin{equation} P = 2C \end{equation} We know that
  • Chickens have two legs
  • Horses and pigs have four legs
So, \begin{equation} 2C + 4H + 4P = 480 \end{equation} We can rewrite the equations as follows: \begin{equation} C = \frac{P}{2} \end{equation} \begin{equation} H = \frac{C}{2} = \frac{P}{4} \end{equation} So, \begin{equation} 2 \frac{P}{2} + 4 \frac{P}{4} + 4P = 480 \end{equation} \begin{equation} 6P = 480 \end{equation} \begin{equation} P = 80 \end{equation}
Asked at: SIG DRW
Category: General View full question page →
Q2

Escalator Steps

Medium
There are two escalators, one moving up and the other moving down at the same constant speed. Two individuals start at the top of each escalator, both walking down at a pace of 1 step per second.
  • The person walking down the downward-moving escalator reaches the bottom after taking 20 steps.
  • The person walking down the upward-moving escalator takes 60 seconds to reach the bottom.
How many steps would each escalator have if they were stationary (i.e., paused)?
Show solution
Let's define the following:
  • T = Total number of steps on an escalator
  • S = Speed of the escalator in steps per second
Next, we can work this problem out using the following equations: \begin{equation} 20 = \frac{T}{S+1} \end{equation} The +1 in this equation accounts for the extra 1 step per second that the person is walking down. The second equation is: \begin{equation} 60 = \frac{T}{-S+1} \end{equation} Here, the S is negative, because the escalator is moving up instead of down. These two equations result in the following: \begin{equation} T = 20S + 20 \end{equation} \begin{equation} T = -60S + 60 \end{equation} Subtracting these two equations from each other results in \begin{equation} 0 = 80S - 40 \end{equation} \begin{equation} S = 0.5 \end{equation} If we substitute S in the first equation, we get that \begin{equation} 20 = \frac{T}{0.5+1} \end{equation} \begin{equation} T = 20*1.5 = 30 \end{equation} So, the escalator has 30 steps.
Asked at: SIG DRW
Category: General View full question page →
Q3

Inflate Rate

Hard
Ginni needs 120 minutes to inflate a massive bouncy castle by herself, while Sheryl would puff away for 150 minutes on her own. They both start inflating a castle together. After 45 minutes of teamwork, Elon jumps in and starts to help inflate as well. With the three of them going at it, the bouncy castle is fully inflated 13 minutes after Elon started helping.

How many minutes would it take Elon to inflate a castle on his own?
Show solution
  • Ginni takes 120 minutes to inflate the castle, so \begin{equation} R_G =  \frac{1}{120}  \end{equation}
  • Sheryl takes 150 minutes to inflate the castle, so \begin{equation} R_S = \frac{1}{150}  \end{equation}
The castle is also inflated if Ginni and Sheryl work together for 45 minutes, and if Elon helps the last 13 minutes, making it a total of 58 minutes. How long would we expect Ginni and Sheryl to take if they had done it together?
  • If you sum up Ginni's and Sheryl's inflation rates, you get \begin{equation} R_{G + S} = \frac{1}{120} + \frac{1}{150} = \frac{3}{200} \end{equation}
  • In other words, we would expect it to take 66.67 minutes to be fully inflated if only Ginni and Sheryl had worked together.
After 45 minutes, the percentage of the castle that Ginni and Sheryl already inflated is equal to: \begin{equation} 45 * \frac{3}{200} = \frac{27}{40} \end{equation} Let's denote Elon's rate as: \begin{equation} R_E = \frac{1}{x} \end{equation} The combined rate for the last 13 minutes is equal to: \begin{equation} R_{G + S + E} = \frac{1}{120} + \frac{1}{150} + \frac{1}{x} \end{equation} Since they completed the remaining $\frac{13}{40}$ of the castle in 13 minutes, their combined rate is equal to: \begin{equation} R_{G + S + E} = \frac{\frac{13}{40}}{13} = \frac{13}{520} \end{equation} Now we have that \begin{equation} R_{G + S + E} = \frac{1}{120} + \frac{1}{150} + \frac{1}{x} = \frac{13}{520} \end{equation} \begin{equation} \frac{1}{x} = \frac{13}{520} - \frac{3}{200} = \frac{1}{100} \end{equation} So, it would take Elon 100 minutes to inflate the castle by his own.
Asked at: SIG DRW
Category: General View full question page →

Why practise these

These puzzles test less your recall of any single method and more whether you can find a way into an unfamiliar problem and reason it through to a clean answer. That instinct is what quant interviews are really checking for, and it is the part that rewards practice over memorisation.

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