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Goldman Sachs·Product Manager·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Goldman Sachs PM interview that threw a digit-sum algorithm problem at me, which felt like a weird left turn for a product role. Not sure what they were testing exactly, maybe just how you think through a technical problem under pressure.

Questions Asked (1)

Q1

Given integers 1 through n representing lottery coupons, a winner is someone whose coupon's digit sum equals some value s. For all valid values of s, find how many distinct values of s produce the maximum number of winners. Implement this as a function and explain the time and space complexity.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

I stared at this for a bit because my first instinct was to just loop through every number, compute digit sums, and tally them up.

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AI HintsAI Generated

Suggested Approach

First, clarify the problem and constraints, then propose an efficient algorithm using digit DP to count winners for each possible digit sum. Analyze the distribution of counts to find the maximum and count how many sums achieve it, and finally discuss time and space complexity.

Pro tip: In product management interviews, always connect the algorithm to business impact—e.g., how this analysis could optimize lottery design or marketing strategies—and mention trade-offs between accuracy and computational cost.

1. Clarify the problem

Restate the problem in your own words, confirm the range of n and s, and ask about constraints (e.g., n up to 10^9).

2. Outline the approach

Explain that you'll use digit DP to count numbers from 1 to n with each possible digit sum, then find the maximum count and how many sums achieve it.

3. Detail the algorithm

Describe the digit DP state (position, sum, tight) and how to iterate over all sums to compute counts. Mention that the maximum digit sum is 9 * number of digits.

4. Analyze complexity

State time complexity O(D * S * 10) where D is number of digits and S is max sum, and space O(D * S).

5. Discuss trade-offs and edge cases

Mention handling n=0 or n=1, and consider if a simpler brute-force is acceptable for small n. Relate to product decisions like scalability.

Key Points to Mention

  • Digit DP for counting numbers with a given digit sum
  • Maximum possible digit sum is 9 * number of digits in n
  • Time complexity O(D * S * 10) and space O(D * S)
  • Edge cases: n=0, n=1, and when multiple sums tie for maximum
  • Trade-off between exact counting and approximation for very large n
  • Business relevance: understanding winner distribution for lottery design

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.