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Moving a knight in the minimal number of moves

Source: Bundeswettbewerb Mathematik 2020, Round 1 - Problem 2

November 17, 2020
combinatoricscombinatorics proposedchess boardChess knight

Problem Statement

Konstantin moves a knight on a n×nn \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 nn do they need the same number of moves?
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