Originally Posted by Prism99

I sketched this out on notecards.

Assuming your fat quarter is 18"x22", your best bet is probably to cut the fat quarter in half first, making 2 pieces that are 18"x11". This will yield 6 rectangles with stripes going one way and 5 rectangles with strips going the other way. If you must have the same number each way, then the most you can get is 5 sets.

If you cut the rectangle in half the other way (so it measures 9"x22"), you get 6 rectangles with stripes going one way but only 4 rectangles with stripes going the other way.

I'm not feeling that great today, so I hope somebody checks my reasoning. You could check it yourself by coloring two sheets of graph paper with stripes; make each graph square 1". Then divide and cut both ways to see if I am right.

If your fat quarters are a different size than 18"x22", all bets are off.