It’s critical to find candidates with math skills when recruiting for finance, technology, and engineering roles.
The math skills of employees can make or break a business, so when you’re hiring skilled people, you should know how to accurately test their math skills.
But have you heard of skills tests? Do you know the right math interview questions to use in your hiring process?
Our list of math skills interview questions below can help you choose your own questions. You’ll also want to stick around for our advice on using skills assessments to hire skilled professionals.
Ever been asked a tricky number theory question in an interview? This post dives into a specific question about weighing combinations with powers of 2, helping you understand the approach and solve it effectively.
The Scenario
Imagine you’re a shopkeeper with six weights 8kg, 4kg, 2kg, 1kg, 1/2kg, and 1/4kg You need to calculate the sum of all possible different combinations of these weights, ensuring no repetition
The Challenge:
At first, this question might seem hard, especially since you are in a hurry for an interview. Don’t worry, though. If you understand the main ideas and follow a methodical approach, you can easily solve this problem.
Key Insights:
- Powers of 2: Notice that all the weights are powers of 2. This crucial detail simplifies the problem significantly.
- Unique Combinations: Since the weights are distinct powers of 2, each combination will have a unique total weight. This eliminates the need to worry about duplicate sums.
- Binary Representation: Each weight combination corresponds to a unique binary representation. For instance, the combination of 2kg, 4kg, and 32kg translates to the binary number 100110.
- Maximum Weight: The largest possible binary number formed using these weights is 111111 (63 in decimal). This means you can weigh any whole number of quarter kilograms from 0 to 63.
Solution Strategies
1 Summation Approach
- Calculate the sum of all individual weights: 8 + 4 + 2 + 1 + 1/2 + 1/4 = 63/4.
- Determine the total number of combinations: 2^6 (since there are 6 weights and each can be included or excluded).
- Multiply the sum by the number of combinations: (63/4) * 2^5 = 504 kg.
2. Binary Representation Approach:
- Recognize that each weight combination corresponds to a unique binary representation.
- The largest possible binary number is 111111, representing a weight of 63/4 kg.
- Calculate the sum of all numbers from 0 to 63: (0 + 1 + 2 + … + 63) = (63 * 64) / 2.
- Convert the sum to kilograms: (63 * 64) / 2 * (1/4) = 504 kg.
3. Duality Approach:
- Observe that every weight has a complementary weight within the set (e.g., 8kg and 1/4kg).
- Since there are 2^6 subsets, pairing them based on complements results in 2^5 unique combinations.
- Multiply the sum of individual weights by the number of unique combinations: (63/4) * 2^5 = 504 kg.
No matter which approach you choose, the answer remains the same: 504 kg.
Remember:
- Clearly explain your chosen approach and reasoning to the interviewer.
- Demonstrate your understanding of number theory concepts and problem-solving skills.
- Stay calm and confident even under pressure.
By mastering this number theory interview question, you’ll showcase your analytical thinking and ability to handle challenging problems effectively.
1 Explain what a cubic meter is.
Based on an object’s length, width, and height, mathematicians use a cubic meter to figure out how much space it takes up. Candidates should know that the unit for cubic meters is “m” raised to the power of three, and they should be able to say that one cubic meter is equal to 1000 liters.
Explain what plane geometry is.
Plane geometry is a branch of mathematics that deals with flat, two-dimensional shapes. The people who are running for office should know that in plane geometry, flat shapes like circles and triangles are put on a two-dimensional plane.
Jane Street quant trading interview question turned into number theory
FAQ
What is the basics of number theory?
What are theoretical interview questions?
How is the number theory used in real life?
What is number theory?
Number Theory is the branch of mathematics that deals with the study of positive numbers and arithmetic operations based on them. Numbers are the mathematical entities that are used for counting. Since the development of human civilization, numbers have always been a source of fascination for various mathematicians across the globe.
What are the key topics in number theory?
Key topics in number theory include prime numbers, divisibility, modular arithmetic, Diophantine equations, and the distribution of prime numbers. Number theory has applications in various fields such as cryptography, computer science, and physics, and it plays a foundational role in many areas of mathematics.
Who invented number theory?
Number Theory or Theory of Numbers is a branch of mathematics that deals with positive numbers and its applications. Who are Credited to have First Developed the Number Theory? People of Babyloian Civilization are credited to have first developed the concept of Number Theory. Who are some popular Number Theorists?
How do I learn number theory?
Take a guided, problem-solving based approach to learning Number Theory. These compilations provide unique perspectives and applications you won’t find anywhere else. Sharpen your skills with these quizzes designed to check your understanding of the fundamentals.
