How many times do you need to fold a piece of paper to make it reach the moon?
You need to fold an average piece of copy paper 42 times in half to reach the moon.
Here's how to figure that out:
The average distance to the moon from Earth's center is 384,403 km, and the average thickness of a sheet of paper is about .1 mm or .0000001 km.
Now, every time we fold the paper, it's thickness will double. When you repeatedly double a quantity, you can calculate what that quantity will be after a certain number of doublings with this formula:
P*2^n
where P is the original quantity, and n is the number of doublings.
Putting our number for paper thickness in:
(.0000001 km)*2^n
we find the number of folds, n, required to reach the moon by simply setting this formula equal to the distance between Earth and the moon and solving for n:
(.0000001 km)*2^n = 384,403km
2^n = 384,403 km/.0000001 km
n = log base 2 (384,403 km/.0000001 km)
n = 41.8058
Since folding only eight tenths of a time doesn't make sense, we round up to 42.