For which positive integers $n$ is it possible to cover a $(2n+1) \times (2n+1)$ chessboard which has one of its corner squares cut out with tiles shown in the figure (each tile covers exactly $4$ squares, tiles can be rotated and turned around)?
Problem
Source: 2003 Estonia National Olympiad Final Round grade 11 p5
Tags: Chessboard, Tiling, combinatorics, rotation