Problem

Source: 2020 IGMO Shortlist (C4) https://artofproblemsolving.com/community/c594864h2364137p19272184

Tags: combinatorics



In chess, a knight moves either two squares vertically and one square horizontally, or two squares horizontally and one square vertically in each move. Suppose a knight can visit every squares on a $4\times n$ chessboard exactly once without repeating. Find all the possible values of $n$.