2023 Pascal Problem 25

Consider positive integers a \le b \le c \le d \le e. There are N lists a, b, c, d, e with a mean of 2023 and a median of 2023, in which the integer 2023 appears more than once, and in which no other integer appears more than once. What is the sum of the digits of N?

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Full credit to this problem is given to the CEMC, you may view all Pascal contests here.