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nxn chessboard cover only with T-tetrominos / Tetris Stones

Source: 8th QEDMO problem 1 (15. 1. 2011) https://artofproblemsolving.com/community/c1512515_qedmo_200507

May 15, 2021
combinatoricscombinatorial geometryChessboard

Problem Statement

A TT-tetromino is a non-convex as well as non-rotationally symmetrical tetromino, which has a maximum number of outside corners (popularly also "Tetris Stone "called). Find all natural numbers nn for which, a n×nn \times n chessboard is found that can be covered only with such TT-tetrominos.
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