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There is a lottery with n coupons and n people take part in it. Each person picks exactly one coupon. Coupons are numbered consecutively from 1 to n, n being the maximum ticket number. The winner of the lottery is any person who owns a coupon where the sum of the digits on the coupon is equal to s. If there are multiple winners, the prize is split equally among them. Determine how many values of s there are where there is at least one winner and the prize is split among most people.
Winning Lottery Ticket
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There is a lottery with n coupons and n people take part in it. Each person picks exactly one coupon. Coupons are numbered consecutively from 1 to n, n being the maximum ticket number. The winner of the lottery is any person who owns a coupon where the sum of the digits on the coupon is equal to s. If there are multiple winners, the prize is split equally among them. Determine how many values of s there are where there is at least one winner and the prize is split among most people.