DE-BUNDESWETTBEWERB 2020 Problem 2

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?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.