Connect four 1x1 squares as shown to get the 5 pieces above, known as tetrominoes inside a rectangle so pieces do not overlap, and the sides are parallel to the rectangle. If the sides of the rectangle have integer lengths, what is the least possible area of the rectangle?
We can arrange them like this so there is only one unused square:
I could not figure out how fit them together so there were no unused squares.
After reading about "tetrominoes" on Wikipedia, I found out that the 5 pieces above are the 5 "free tetrominoes," and "Although a complete set of free tetrominoes has a total of 20 squares, they cannot be packed into a rectangle." See:
the least possible area of the rectangle = 3 * 7 = 21 squares