MathDB

4

Part of 2023 Balkan MO

Problems(1)

Sum of some numbers of a set is equal to the sum of some of the rests

Source: BMO 2023 Problem 4

5/10/2023
Find the greatest integer k≤2023k\leq 2023 for which the following holds: whenever Alice colours exactly kk numbers of the set {1,2,…,2023}\{1,2,\dots, 2023\} in red, Bob can colour some of the remaining uncoloured numbers in blue, such that the sum of the red numbers is the same as the sum of the blue numbers.
Romania
BMO 2023combinatorics