MathDB
Plus or Minuses

Source: OMM 2009 4

July 15, 2014
combinatorics unsolvedcombinatorics

Problem Statement

Let n>1n>1 be an odd integer, and let a1a_1, a2a_2, …\dots, ana_n be distinct real numbers. Let MM be the maximum of these numbers and mm the minimum. Show that it is possible to choose the signs of the expression s=±a1±a2±⋯±ans=\pm a_1\pm a_2\pm\dots\pm a_n so that
m<s<Mm<s<M
Back to ProblemsView on AoPS