Faulty Bricks

[From the notes of Emily Moore. Modified slightly by Sam Rebelsky.]

Many building bricks are twice as long as they are wide. I need to pile some up in a rectangular pile until I am ready to use them, and I would like to do it in such a way that each layer is free of any fault line going between two layers.

What sizes can I make the layers?

By fault line we mean a continuous straight line from left edge to right edge that runs between two layers.