Problem

Source: Iranian RMM TST 2021 Day2 P1

Tags: combinatorics, square grid



A polyomino is region with connected interior that is a union of a finite number of squares from a grid of unit squares. Do there exist a positive integer $n>4$ and a polyomino $P$ contained entirely within and $n$-by-$n$ grid such that $P$ contains exactly $3$ unit squares in every row and every column of the grid? Proposed by Nikolai Beluhov