Problem

Source: Bundeswettbewerb Mathematik 2020, Round 1 - Problem 2

Tags: combinatorics, combinatorics proposed, chess board, Chess knight



Konstantin moves a knight on a $n \times n$- chess board from the lower left corner to the lower right corner with the minimal number of moves. Then Isabelle takes the knight and moves it from the lower left corner to the upper right corner with the minimal number of moves. For which values of $n$ do they need the same number of moves?