Out of Reach
Burj Khalifa is currently the highest building in the world with the height of 829.8 meters, and you're thinking of a very odd way to reach its top.
That is, you want to fold a gigantic piece of paper of 0.1 millimeter thickness multiple times to increase the height of the folded paper vertically. Every time you fold the paper in halves, the total paper thickness doubles, and the paper's area is so infinite that you can continue folding as many times as you'd like.
At least how many times will you need to fold such paper so that it can surpass the top of the building?
The answer is 23.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
When we fold the paper for n times, the total height(thickness) = 0 . 0 0 0 1 × ( 2 n ) meters.
In order to reach the top of the building, we can equalize the building's height with the exponent:
0 . 0 0 0 1 × ( 2 n ) meters = 829.8 meters
2 n = 8298000
n = l o g 2 l o g 8 2 9 8 0 0 0 ≈22.98
Therefore, to surpass the top, we need to fold the paper at least 23 times.