MathDB
Solution set of an inequality - Austria 2010

Source:

May 13, 2010
inequalitiesfunctionalgebra proposedalgebra

Problem Statement

For a positive integer nn, we define the function fn(x)=∑k=1n∣x−k∣f_n(x)=\sum_{k=1}^n |x-k| for all real numbers xx. For any two-digit number nn (in decimal representation), determine the set of solutions Ln\mathbb{L}_n of the inequality fn(x)<41f_n(x)<41.
(41st Austrian Mathematical Olympiad, National Competition, part 1, Problem 2)
Back to ProblemsView on AoPS