Question 5
A function $f:\mathbb R\to\mathbb R$ is essentially increasing if $f(s)\le f(t)$ whenever $s\le t$ and both values are nonzero. Find the smallest integer $k$ such that for any real numbers $x_1,\ldots,x_{2022}$ there are $k$ essentially increasing functions with
$$\sum_{i=1}^k f_i(n)=x_n\quad(1\le n\le2022).$$
Proposed by Gabriel Carroll. Source: Evan Chen’s third-party solution notes; https://aops.com/community/p24774633. One point is a nonofficial editorial normalization; this essay requires manual grading.
$$\sum_{i=1}^k f_i(n)=x_n\quad(1\le n\le2022).$$
Proposed by Gabriel Carroll. Source: Evan Chen’s third-party solution notes; https://aops.com/community/p24774633. One point is a nonofficial editorial normalization; this essay requires manual grading.