There are 8 ways to fold a 2 × 2 map along its creases:

But no one knows how to calculate the number of ways that a larger map might be folded. Amazingly, the number of ways to fold an n × n map has been worked out only as high as 7 × 7:

1, 8, 1368, 300608, 186086600, 123912532224, 129950723279272

Via Fermat’s Library.