## Map Folding

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

See also Stamp Folding

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 Eric W. Weisstein
1999-05-26