MathDB
Sum of 16 < Sum of 10

Source: May Olympiad 2021 #5 L1

August 16, 2021
number theory

Problem Statement

Bob writes 3636 consecutive positive integers in a white paper(in ascending order), next he computes the sum of digits of each one of 3636 numbers(in the order) and writes the first 1616 results in a red paper and the last 1010 results in a blue paper. Determine if Bob can choose the 3636 integers, such that the sum of the numbers in the red paper is less than or equal to sum of the numbers in the blue paper.