Question 56
For a positive integer $n$, let $f_n(x)$ be defined by
$$
f_n(x) = \sum_{k=1}^{n} |x - k|.
$$
Determine the solution to the inequality $f_n(x) \lt 41$ for every two-digit integer $n$ (in decimal notation).
G. Baron, Vienna
$$
f_n(x) = \sum_{k=1}^{n} |x - k|.
$$
Determine the solution to the inequality $f_n(x) \lt 41$ for every two-digit integer $n$ (in decimal notation).
G. Baron, Vienna