2

Part of 2010 Federal Competition For Advanced Students, Part 1

Problems(1)

Solution set of an inequality - Austria 2010

Source:

For a positive integer

n

, we define the function

f_n(x)=\sum_{k=1}^n |x-k|

for all real numbers

x

. For any two-digit number

n

(in decimal representation), determine the set of solutions

\mathbb{L}_n

of the inequality

f_n(x)<41

.
(41st Austrian Mathematical Olympiad, National Competition, part 1, Problem 2)

inequalitiesfunctionalgebra proposedalgebra