Can you solve this puzzle?
An ant leaves its anthill in order to forage for food. It moves with the speed of 10cm per second, but it doesn't know where to go, therefore every second it moves randomly 10cm directly north, south, east or west with equal probability.
- If the food is located on east-west lines 20cm to the north and 20cm to the south, as well as on north-south lines 20cm to the east and 20cm to the west from the anthill, how long will it take the ant to reach it on average?
- What is the average time the ant will reach food if it is located only on a diagonal line passing through (10cm, 0cm) and (0cm, 10cm) points?
- Can you write a program that comes up with an estimate of average time to find food for any closed boundary around the anthill? What would be the answer if food is located outside an defined by ( (x – 2.5cm) / 30cm )2 + ( (y – 2.5cm) / 40cm )2 < 1 in coordinate system where the anthill is located at (x = 0cm, y = 0cm)? Provide us with a solution rounded to the nearest integer.
Did you like this puzzle? Are you looking for bigger challenges? Do you want to use your analytical skills to solve real world problems and see the results right away? Do you enjoy writing computer programs? Then the Quantitative Researcher position might be a great opportunity for you!
What you’ll do
As a Quantitative Researcher you will work in a team with Traders and Researchers, right on the trading floor. You will spend your first weeks at Optiver in a structured training program to learn about options, market making and delta 1. You will then immediately start your first project, with the support of a Senior Researcher. We expect you to be versatile, flexible and very creative to think of new innovative solutions. In return we give you the freedom to pursue your ideas and implement them right into our production systems. Within a few months, you will play a key role in developing automated analysis programs and trading algorithms.
What you'll need
- Academic degree with very good grades in Engineering, Physics, Maths, Econometrics, Computer science or equivalent
- Programming experience in any language (C, C++, Python, Basic, JAVA, etc.);
- Ability to apply basic concepts of probability, calculus and linear algebra;
- Ability to carry a project on your own in a structured way within a short timeframe;
- Competitive attitude and eagerness to constantly improve yourself;
- Self-starting, ‘can do’ attitude;
- Ability to learn quickly;
- Excellent verbal and written English skills.
What you’ll get
- The chance to start your career working alongside best-in-class professionals from over 40 different countries.
- Our performance based bonus structure is unmatched anywhere in the industry. We combine our profits across desks, teams and offices into a global profit pool fostering a truly collaborative environment to work in.
Alongside this you will get great secondary benefits such as 25 paid vacation days, fully paid first-class commuting expenses, training opportunities, discounts on health insurance, breakfast and lunch facilities, sports and leisure activities, Friday afternoon drinks and even weekly in-house chair massages. Being highly international, we are accustomed to guiding expats through their relocation, offering competitive relocation packages and providing visa sponsorship where necessary.
Are you interested in starting your career on one of the most dynamic and exciting trading floors in Europe?
Apply directly via our website for the position of Quantitative Researcher. Please provide us with a CV, a solution to all three puzzle questions highlighting in bold your final answers and a letter of motivation in English. Applications without an answer to the puzzle and a letter of motivation will not be reviewed.
The full puzzle solution is to be uploaded in the same document as the cover letter and submitted as a pdf.
If you have any questions feel free to contact the recruitment team on [email protected] or on +31 (0)20 708 70 00.
Kindly note that we do not require any assistance from third-parties including agencies in the recruitment of this role.