A piece of paper is folded in half, creating two layers of paper. The paper is then folded in half again. This is continued until the paper has been folded in half a total of five times. The total number of layers of paper in the folded sheet is
Problem 243
Pick one
Official solution
The first fold creates 2 layers of paper. The second fold places 2 sets of 2 layers together, for a total of 4 layers of paper. Similarly, the third fold places 2 sets of 4 layers of paper together, for a total of 8 layers of paper.
That is, each new fold places 2 sets of the previous number of layers together, thereby doubling the previous number of layers.
The results of the first five folds are summarized in the table below.
| Number of folds | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Number of layers | 1 | 2 | 4 | 8 | 16 | 32 |
After the sheet has been folded in half five times, the number of layers in the folded sheet is 32.