What I've done so far is fashion a cardboard footprint. I had to glue two 8.5" x 11" pieces (which, for those math phobes out there, makes 17" x 22") and made up the rest with strips. Then, I surrounded the perimeter with full coffee stirrers, and I will painstakingly and hopefully patiently glue the tiny, tiny strips of wood into a zigzag pattern. Let's do the math, shall we?
Area of floor: 360 square inches (minus around 7 square inches for the cutout for the stair landing)
Area of one wood strip: 0.1640625 square inches (dimensions 3/16" x 7/8" or 0.1875" x 0.875")
Number of wood strips needed to cover floor: 360 ÷ 0.1640625 = 2194