MathDB
coloring nice sets

Source: RMO District 2005, 12th Grade, Problem 1

March 5, 2005
inductioncombinatorics proposedcombinatorics

Problem Statement

Let A1A_1, A2A_2, …\ldots, AnA_n, n≥2n\geq 2 be nn finite sets with the properties i) ∣Ai∣≥2|A_i| \geq 2, for all 1≤i≤n1\leq i \leq n; ii) ∣Ai∩Aj∣≠1|A_i\cap A_j| \neq 1, for all 1≤i<j≤n1\leq i<j\leq n. Prove that the elements of the set ⋃i=1nAi\displaystyle \bigcup_{i=1}^n A_i can be colored with 2 colors, such that all the sets AiA_i are bi-color, for all 1≤i≤n1\leq i \leq n.
Back to ProblemsView on AoPS