There is a new company, Tile Carpets, that sells carpets as individual tiles that can be laid down side by side to form a single solid plane. These pieces of carpet are sold in sets, where every piece in the set is the same shape and size.
In order to form a single carpet, customers arrange the carpet tiles on the floor with no gaps in between them. This is possible for some shapes, but not for others. Which of the following shapes is impossible to lay down with no gaps?