Here's a high-backed chair that breaks down flat and has no pegs or wedges to keep up with. You can get two chairs out of a 4'x8' sheet of plywood. (Click on the photo for an enlarged image.) This one was made with 3/4" plywood.
Section A matches section B. These are the legs.
Assemble A, B, and D (seat), and slide C (back) into slots on the top of A & B and the slot on D. Slot (E) is slightly angled to accomodate the slant of the seat and back; this will lock the chair together.
These diagrams are exact relative measurements. Print out and enlarge the images to 24" square each, with the exception of C (the back) which is 36" tall and 24" wide.