Y by cubres
Exactly
cells of an
square grid are colored black, and the remaining cells are white. The cost of such a coloring is the minimum number of white cells that need to be recolored black so that from any black cell
, one can reach any other black cell
through a sequence
of black cells where each consecutive pair
are adjacent (sharing a common side) for every
. Let
denote the maximum possible cost over all initial colorings with exactly
black cells. Determine a constant
such that
for any
.










![\[
\frac{1}{3}n^{\alpha} \leq f(n) \leq 3n^{\alpha}
\]](http://latex.artofproblemsolving.com/0/a/0/0a06d4ff52479c8cb785c6450cea8748bf7769b6.png)

This post has been edited 1 time. Last edited by Assassino9931, Apr 9, 2025, 8:54 AM