16. The sum of 2023 consecutive integers is 2023 . What is the sum of digits of the largest of these integers?
A 4
B 5
C 6
D 7
E 8
Solution
A

Let the middle integer of the list be $n$. Since the 2023 digits are consecutive, the complete list is $n-1011, n-1010, \ldots, n-1, n, n+1, \ldots, n+1010, n+1011$ with sum $2023 n$. Therefore $2023 n=2023$ and so $n=1$. Hence the largest integer of the list is $1+1011=1012$, which has digit sum 4 .