MathDB

C2

Part of 2019 Pan-African Shortlist

Problems(1)

Replace two numbers with sum of digits of their sum

Source: 2019 Pan-African Shortlist - C2

1/18/2021
On the board, we write the integers 1,2,3,…,20191, 2, 3, \dots, 2019. At each minute, we pick two numbers on the board aa and bb, delete them, and write down the number s(a+b)s(a + b) instead, where s(n)s(n) denotes the sum of the digits of the integer nn. Let NN be the last number on the board at the end.
[*] Is it possible to get N=19N = 19? [*] Is it possible to get N=15N = 15?
number theorycombinatoricssum of digits