It sounds a little like the quick trip around the world quilt by Eleanor Burns. After you sew the tubes together, on one tube set you cut at the seam, on the next tube set you cut in the middle of the strip. That's what makes your seams offset each other. It gives kind of a stairstep effect. That's the way I did the strips on this quilt for my sil.
http://www.quiltingboard.com/t-3580-1.htm