20. The positive integer $N$ is the smallest one whose digits add to 41 . What is the sum of the digits of $N+2021$ ?
A 10
B 12
C 16
D 2021
E 4042
Solution
A

The smallest positive integer $N$ whose digits add to 41 has as few digits as possible and then as small a digit as possible as its first digit. Hence as many digits as possible, except for the first digit, should be 9 . Since $41=4 \times 9+5$, we have $N=59999$. Therefore the value of $N+2021$ is 62020 with digit sum $6+2+2=10$.