At first the title of this post might seem ridiculous but its true. If it was possible to fold a sheet of paper 42 times it would be thick enough to reach the moon. Here is the explanation
Each time you fold a paper it doubles in thickness. Zero folds=1 sheets tick, one fold=2 sheets thick, two folds=4 sheets thick. This follows the rule where the thickness (in sheets) is equal to two raised to the number of folds or
To convert from number of sheets thick to a dimension we just multiply by the thickness of one sheet (varies by type but .1mm is a good average). Where .1mm is 10-4 meters. So thickness in meters is given by the equation
So if we want the thickness to be the distance to the moon (3.939*108 meters) we plug that into the equation and solve for # of folds
3.939*1012=2#folds :solving for an exponent requires that we take the natural log of both sides so we can pull the exponent down
# folds=ln (3.939*1012)/ln(2)
# folds=41.8 :You can't take .8 folds of something so we have to round up to 42 folds
So if we fold a paper 42 times it's thickness is going to be given by the following equation
T=4.39 *108 meters
So it actually extends past the moon by 45,000km or 28,000 miles.
As a note its very hard to fold paper more than 7 times, or anything more than 13 times. I don't think anythings been folded more than 15 times, certainly not 20 and 42 times is easily impossible.