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

t(sheets)=2

^{#folds}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 equationT(m)=(10

^{-4})*2^{#folds}So if we want the thickness to be the distance to the moon (3.939*10

^{8}meters) we plug that into the equation and solve for # of folds3.939*10

^{8}=(10^{-4)}*2^{#folds}3.939*10

^{12}=2^{#folds }:solving for an exponent requires that we take the natural log of both sides so we can pull the exponent downln(3.939*10

^{12})=ln(2^{#folds})ln(3.939*10

^{12})=#folds*ln(2)# folds=ln (3.939*10

^{12})/ln(2)# folds=41.8 :You can't take .8 folds of something so we have to round up to 42 folds

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So if we fold a paper 42 times it's thickness is going to be given by the following equation

T=10

^{-4}*2^{42}metersT=4.39 *10

^{8}metersSo 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.

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