Adding an illustration to help with understanding

[fidian]

The number order takes much longer to understand than an image.

I created this image by starting with AI (no copyright) and then I made many updates. I release this image into the public domain, in case it matters. Use it if you like in any way you like.

[Hoatzin]

This is indeed really helpful. My only note here is that the order of stacking in the two illustrations as colored is not consistent. Namely, on the saddle stitch, the second signature generated is purple, while in the perfect binding the second signature is blue. We might also want to put some page numbers on the designs (for at least the pages that are facing the viewer in the diagram) that align with the baffling numbers you are fixing here, ie 4,1,2,3 or 8,1,2,7/6,3,4,5 xor 4,1,2,3 or 4,1,2,3/8,5,6,7.