A general Formula giving the number of distinct ways of folding an rectangular map is not known. A distinct folding is defined as a permutation of numbered cells reading from the top down. Lunnon (1971) gives values up to .

1 | 1 | 1 | |||

2 | 2 | 8 | |||

3 | 6 | 60 | 1368 | ||

4 | 16 | 1980 | 300608 | ||

5 | 59 | 19512 | 18698669 | ||

6 | 144 | 15552 |

The limiting ratio of the number of strips to the number of strips is
given by

**References**

Gardner, M. ``The Combinatorics of Paper Folding.'' Ch. 7 in *Wheels, Life, and Other Mathematical Amusements.*
New York: W. H. Freeman, 1983.

Koehler, J. E. ``Folding a Strip of Stamps.'' *J. Combin. Th.* **5**, 135-152, 1968.

Lunnon, W. F. ``A Map-Folding Problem.'' *Math. Comput.* **22**, 193-199, 1968.

Lunnon, W. F. ``Multi-Dimensional Strip Folding.'' *Computer J.* **14**, 75-79, 1971.

© 1996-9

1999-05-26