Counting Questions at MathWorks: What to Expect

Counting questions appear in about 10% of MathWorks' technical interview problem set. While this may seem like a small portion, these problems test a candidate's fundamental grasp of discrete mathematics, logical structuring, and ability to translate a word problem into clean, efficient code. Success here signals strong analytical thinking—a core competency for roles involving algorithm development, simulation, or data processing at MathWorks.

What to Expect — Types of Problems

MathWorks counting problems typically involve enumerating possibilities under specific constraints. You won't see abstract combinatorics formulas in isolation. Instead, expect applied scenarios where you must derive the counting logic yourself. Common themes include:

• Sequential Choices: Counting the number of valid sequences, passcodes, or paths (e.g., "count all 4-digit codes where no digit repeats and the first digit is not zero").
• Subset Enumeration: Counting subsets that meet a condition, often without generating all subsets explicitly (e.g., "count the number of non-empty subarrays with a sum less than k").
• Combinatorial Arrangements: Problems involving permutations, combinations, or the "stars and bars" method, usually framed within a tangible context like distributing resources or arranging items.

The key challenge is identifying the correct counting principle and implementing it without double-counting or missing cases.

How to Prepare — Study Tips with One Code Example

Focus on the logic, not just memorization. For each problem type, practice by:

1. Writing out small examples by hand to spot the pattern.
2. Stating the counting rule in plain English before coding.
3. Considering edge cases (empty sets, minimum/maximum values).

A frequent pattern is using iterative accumulation or dynamic programming to build counts, as seen in this classic problem: Count the number of ways to climb n stairs taking 1 or 2 steps at a time.

def climb_stairs(n):
    if n <= 2:
        return n
    dp = [0] * (n + 1)
    dp[1], dp[2] = 1, 2
    for i in range(3, n + 1):
        dp[i] = dp[i - 1] + dp[i - 2]
    return dp[n]

This demonstrates how a counting problem (Fibonacci-like sequence) is solved by building up from base cases.

Recommended Practice Order

1. Start with foundational combinatorics: permutations, combinations, and the multiplicative principle.
2. Move to basic coding problems that implement these directly (e.g., generating combinations).
3. Practice applied word problems that require you to model the scenario as a counting pattern.
4. Finally, tackle mixed problems where counting is combined with other concepts like constraints or optimization.

Consistent practice in translating narrative constraints into precise counting logic is the most effective preparation.

Practice Counting at MathWorks