Folding a Strip of Labeled Stamps
This Demonstration illustrates the different ways a strip of stamps labeled 1 through can be folded into a stack one stamp wide. In each figure, the colored lines represent the stamps and the dotted lines represent the perforation between adjacent stamps.
Snapshot 1: for 1, 2, and 3 stamps, the number of labeled stamp foldings is equal to the number of permutations of items, or
Snapshots 2, 3: for stamps, the number of labeled stamp foldings is less than , since some permutations lead to impossible foldings; for example, is an impossible folding, since the perforation joining stamps 1 and 2 would intersect with the perforation joining 3 and 4
M. Gardner, "The Combinatorics of Paper Folding," Wheels, Life and Other Mathematical Amusements, New York: W. H. Freeman, 1983 pp. 60–61.