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the folding challenge

until just a few years ago it was deemed impossible to be able to fold anything (paper, in particular) in half more than 7 or 8 times.

Assuming it were possible to fold paper without restriction, the height of a piece of folder paper would double in thickness each time it was folded. Since one sheet of typical 20-pound paper has a thickness of about 0.1 millimeter, folding 50 times (if this were physically possible, which of course it is not) would produce a wad of height 1.13×10^(11) meters, and folding one more time would make the stack higher than the distance between the Earth and Sun.

a California high school junior beat this challenge with 9, 10, 11, 12 folds and derived the mathematical limits describing how it can be done.
link to Mathworld article