Lottery Coupon Winners Calculation
Overview
This question evaluates algorithmic counting and combinatorics skills, focusing on frequency analysis of digit-sum distributions and reasoning about time and space complexity.
Goldman Sachs
Jul 4, 2025, 8:28 PM
Product Manager
Take-home Project
Product / Decision Making
4
0
Lottery Coupons: Most Popular Digit-Sum Values
Problem
You have consecutively numbered lottery coupons from 1 to n (inclusive). A coupon is a winner if the sum of its digits equals some value s.
Among all valid digit sums s in the range 1 to 9·d, where d is the number of digits of n, determine how many distinct s values produce the maximum number of winners (i.e., the most frequent digit-sum(s) among coupons 1…n).
Implement a function lotteryCoupons(n) that returns this count, and explain the algorithm’s time and space complexity.
- Assume n ≥ 1 and base-10 representation.
- Note: Values of s that are not achievable for 1…n simply have zero winners and do not affect the maximum.
Hints
- Only the frequency of each digit-sum matters; you do not need to materialize each coupon.
- Think about how to compute digit-sum frequencies efficiently for the range 1…n.
Solution
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