Removing a unit square from a $2\times 2$ square we get a piece called L-tromino. From the fourth line of a $7 \times 7$ cheesboard some unit squares have been removed. The resulting chessboard is cut in L-trominos. Determine the number and location of the removed squares.
I'm pretty sure any location in the 4th line can be removed, if there is only one square removed.
Also, note that there must be exactly 4 L-trominoes that are in the 1st row, and that then leaves two unused squares in the 2nd row. It's possible to prove with casework that the number of L -trominoes that occupy both row 3 and 4 is at least 3.
By symmetry, this forces there to be at least 6 L-trominoes that have a piece in the 7th row. Therefore, there must be at most one unoccupied square in the 7th row. Finding configurations for this is left to the reader.