Paper Cutting Through Flaps
Consider a standard rectangular paper with positive length and width values. Let denote the nonnegative number of consecutive single-direction folding (in half) from the start. Then, consider the following pattern that involves a straight cut parallel to the folds:
If , then we cut into 2 smaller pieces of paper .
If , then we have a paper folded in half. Cutting past the overlapped flaps gives us 3 smaller pieces .
If , then we have a paper folded two times. Cutting gives us 5 smaller pieces .
How many smaller pieces do we have if we cut the folded paper that is folded times from the start?
The answer is 32769.
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
Observing the number of pieces we get for each value of n we get
n=1,p=3 .
n=2,p=5 .
n=3,p=9
n=4,p=17 .
This follows the sequence p= 2 n +1
Thus for n=15 p= 32769. .
. .
(This sequence arises because each fold multiplies the cut by 2 thus the cut forms 2 n cuts when the paper is opened. And for 2 n cuts there would be 2 n +1 pieces of paper.) .