Can we tile a 75 \times 75 by using domino tiles(2 \times 1) or a plus piece (a piece with 5 cells with the shape of a plus sign)
Color the 75 \times 75 board in a checkerboard coloring.
WLOG assume that the number of black squares exceeds the number of white squares by 1.
Let a and b be the numbers of black and white squares covered by the placed pieces, respectively.
A domino covers exactly 1 black and 1 white square, so the difference a-b does not change.
A plus piece covers either 4 black squares and 1 white square, or 4 white squares and 1 black square.
Thus, placing a plus piece changes a-b by \pm 3.
Therefore, a-b is always divisible by 3.
However, in the end, the difference between black and white squares on the board is 1 contradiction.
Hence, it is impossible to tile the 75 \times 75 board with these pieces.