Hi Dena -- Glad you asked because I LOVE math.

The short answer is YES, you could cut the colored strips from the 20 fat quarters you have. In fact, if you are careful and precise, you could get all those strips from just 13 fat quarters.

Now for the long answer.
The pattern asks for-
-- (48) 8" strips: Using 3 fat quarters, cut parallel to the short side. Cut (24) 2.5" strips (these will each be 18" long). Cut these (24) strips into two 8" strips each.
-- (48) 12.5" strips: Using 3 fat quarters, cut parallel to the long side. Cut (16) 2.5" strips (each will be 40" long). Cut these 16 strips into three 12.5" strips each.
-- (96) 9.5" strips: Using 3 fat quarters, cut parallel to the long side. Cut (28) 2.5" strips (each will be 40" long). Cut these 28 strips into four 9.5" strips each.
-- (96) 11" strips: Using 4 fat quarters, cut parallel to the long side. Cut (32) 2.5" strips (each will be 40" long). Cut these 32 strips into three 11" strips each.

I think that I would be a little looser than the measurements I've given you, because you probably want to use all 20 colors that you have. So when I suggest using four fat quarters, you may want to use six or eight different colors just to mix up the colors more. Definitely think about using three different colors for that first set of 8" strips, because those get cut from the short side, not the long side.

Good luck! And please post a photo when you've made this quilt top. I love the pattern you've chosen.