Question 2
An $n \times n$ ($n \ge 4$) square is divided into $n^2$ unit cells. Find all possible values of $n$ such that this square can be covered with some layers of 4-cell figures of the following shape [ ] (i.e. each cell of the square must be covered with the same number of these figures).
(The sides of each figure must coincide with the sides of the cells; the figures may be rotated but none of them can go beyond the bounds of the square.)
(Jury)
Editorial source clarification: The original Belarus 2014 booklet, problem 8.8, shows a straight $1\times4$ rectangle (I-tetromino) at the bracket placeholder, not an L-tetromino. This independently recovered definition supplements the unchanged extraction above.
(The sides of each figure must coincide with the sides of the cells; the figures may be rotated but none of them can go beyond the bounds of the square.)
(Jury)
Editorial source clarification: The original Belarus 2014 booklet, problem 8.8, shows a straight $1\times4$ rectangle (I-tetromino) at the bracket placeholder, not an L-tetromino. This independently recovered definition supplements the unchanged extraction above.