MathDB
{1, 2, . . . , 20} has at least 2018 sumfree subsets

Source: 2018 Chile National Olympiad level 2 p5

October 22, 2022
combinatorics

Problem Statement

Consider the set Ω\Omega formed by the first twenty natural numbers, Ω={1,2,...,20}\Omega = \{1, 2, . . . , 20\} . A nonempty subset AA of Ω\Omega is said to be sumfree [/i ] if for all pair of elementsx,y∈A x, y \in A, the sum (x+y)(x + y) is not in AA, ( xx can be equal to yy). Prove that Ω\Omega has at least 20182018 sumfree subsets.
Back to ProblemsView on AoPS