MathDB

On the board, we write the integers

1, 2, 3, \dots, 2019

. At each minute, we pick two numbers on the board

a

and

b

, delete them, and write down the number

s(a + b)

instead, where

s(n)

denotes the sum of the digits of the integer

n

. Let

N

be the last number on the board at the end.
[*] Is it possible to get

N = 19

? [*] Is it possible to get

N = 15

Problem Statement