MathDB
Subset A satisfies two given conditions

Source: Romanian TST 1998

April 23, 2011
floor functioncombinatorics proposedcombinatorics

Problem Statement

Let n≥2n\ge 2 be an integer. Show that there exists a subset A∈{1,2,…,n}A\in \{1,2,\ldots ,n\} such that:
i) The number of elements of AA is at most 2⌊n⌋+12\lfloor\sqrt{n}\rfloor+1
ii) {∣x−y∣∣x,y∈A,x≠y}={1,2,…n−1}\{ |x-y| \mid x,y\in A, x\not= y\} = \{ 1,2,\ldots n-1 \}
Radu Todor
Back to ProblemsView on AoPS