Lottery Coupons

• The idea is you're given n integer n which denotes 2 things
  1. the number of lottery coupons, (all numbered consecutively from 1 to n)
  2. the number of people taking part in the lottery; each person will receive exactly 1 coupon
• Someone wins when their coupon's digits have a sum equal to s.
• If there's multiple winners, the prize is split equally among them.
• The end goal is to determine how many values of s there are where at least one person wins and the prize is split amongst the most people.

Example

• The value of n is 12
• The list of coupon numbers generated from 1 to n is [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12].
• The sums of the digits are [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3].
• The largest number of winners is 2 which will occur for coupons numbered [1, 10], [2, 11] and [3, 12].
• The maximum number of possible winners occurs for any of these 3 possible values of s, so 3 is the answer.