Problem

Source: Romania JBMO TST 2024 Day 1 P5

Tags: combinatorics, board



An $n$-type triangle where $n\geqslant 2$ is formed by the cells of a $(2n+1)\times(2n+1)$ board, situated under both main diagonals. For instance, a $3$-type triangle looks like this:Determine the maximal length of a sequence with pairwise distinct cells in an $n$-type triangle, such that, beggining with the second one, any cell of the sequence has a common side with the previous one. Cristi Săvescu