MathDB
2022 Junior Balkan MO, Problem 4

Source: 2022 JBMO Problem 4

June 30, 2022
combinatoricssets of integerspartitions

Problem Statement

We call an even positive integer nn nice if the set {1,2,…,n}\{1, 2, \dots, n\} can be partitioned into n2\frac{n}{2} two-element subsets, such that the sum of the elements in each subset is a power of 33. For example, 66 is nice, because the set {1,2,3,4,5,6}\{1, 2, 3, 4, 5, 6\} can be partitioned into subsets {1,2}\{1, 2\}, {3,6}\{3, 6\}, {4,5}\{4, 5\}. Find the number of nice positive integers which are smaller than 320223^{2022}.
Back to ProblemsView on AoPS