MathDB
Set with 2008 elements

Source: RMO 2008, Grade 10, Problem 3

April 30, 2008
modular arithmeticcombinatorics proposedcombinatorics

Problem Statement

Let A\equal{}\{1,2,\ldots, 2008\}. We will say that set X X is an r r-set if ∅≠X⊂A \emptyset \neq X \subset A, and ∑x∈Xx≡r(mod3) \sum_{x\in X} x \equiv r \pmod 3. Let Xr X_r, r∈{0,1,2} r\in\{0,1,2\} be the set of r r-sets. Find which one of Xr X_r has the most elements.
Back to ProblemsView on AoPS