Make Mbius strips from long slim rectangles R of grid paper (graph paper) by pasting the short sides together after giving the paper a half-

Make Möbius strips from long slim rectangles R of grid paper (graph paper) by pasting the short sides together after giving the paper a half- twist. In each case count the number of parts obtained by cutting along lines parallel to the edge.

(a) Make R three squares wide and cut until you reach the beginning.

(b) Make R four squares wide. Begin cutting one square away from the edge until you reach the beginning. Then cut the portion that is still two squares wide.

(c) Make R five squares wide and cut similarly.

(d) Make R six squares wide and cut. Formulate a conjecture about the number of parts obtained.