Was that answer expected?

Algebra Level 3

How many times do you have to fold a paper, so that it can reach the moon?

Details and Assumptions

Assume that the paper is of uniform thickness i.e. 0.01 cm

The distance from the Earth to the moon is $3.84 \times {{10}^{12}}$ pages, If piled one over the other,

Assume that you can Fold a paper as many times as you like. (Good luck folding it more than 8 times in reality)

You fold the paper in half every time.

2 solutions

Mehul Arora
Jun 12, 2015

When we Fold a paper, It's thickness becomes twice.

Therefore, After the ${n}^{th}$ operation, The thickness of the paper will be ${2}^{n}$

We have to find the smallest $n$ such that

${2}^{n} >3.42 \times {10}^{12}$

We take $log_2$ on both sides.

Therefore $n= log_2 {3.42 \times {10}^{12}}= 41.637133 (approx)$

Hence, 42 folds of a paper are required to reach the mon from Earth.

Enjoy! :D

Heitor Vinícius
Sep 29, 2015

Excuse me, I didn't understand one thing. Where did $3.42 \times 10^{12}$ come from? Thanks in advance.