This mystery quilt uses a Layer Cake. Layer Cakes are collections of 10″ x 10″ squares of fabric made by Moda Fabrics. Layer Cakes typically include 42 pieces of fabric, although the number may vary. You need one Layer Cake (or a similar collection of about 40 cuts of 10″ squares).
You can also make this quilt with yardage or even scraps!
I give requirements below for each of the three ways.