Lucas (1891) credits the invention of the stamp folding problem to Émile Lemoine.
[3] The number of different ways to fold a strip of n stamps is given by the sequence These numbers are always divisible by n (because a cyclic permutation of a foldable stamp sequence is always itself foldable),[3][4] and the quotients of this division are the number of topologically distinct ways that a half-infinite curve can make n crossings with a line, called "semimeanders".
In the 1960s, John E. Koehler and W. F. Lunnon implemented algorithms that, at that time, could calculate these numbers for up to 28 stamps.
[5][6][7] Despite additional research, the known methods for calculating these numbers take exponential time as a function of n.[8][9] Thus, there is no formula or efficient algorithm known that could extend this sequence to very large values of n. Nevertheless, heuristic methods from physics can be used to predict the rate of exponential growth of this sequence.
However, according to the solution of the carpenter's rule problem, every folded state can be constructed (or equivalently, can be unfolded).
However, the general problem of counting the number of ways to fold a map remains unsolved.