Lottery Coupon Winners Calculation
Company: Goldman Sachs
Role: Product Manager
Category: Product / Decision Making
Difficulty: medium
Interview Round: Take-home Project
##### Question
You are given an integer n representing consecutively numbered lottery coupons from 1 to n. A person is considered a winner if the sum of the digits on their coupon equals a value s. Among all possible values of s (1 ≤ s ≤ 9·⌈log10 n⌉), determine how many distinct values of s yield the largest possible number of winners. Implement a function lotteryCoupons(n) that returns this count, and explain your algorithm’s time- and space-complexity.
##### Hints
Observe that only the frequency of each digit-sum matters; you do not need to materialize every coupon number.
Think about how to compute digit sums efficiently for the range 1…n.
Quick Answer: This question evaluates algorithmic counting and combinatorics skills, focusing on frequency analysis of digit-sum distributions and reasoning about time and space complexity.