Zara’s bicycle tire has a circumference of 1.5 m. If Zara travels 900 m on her bike, how many full rotations will her tire make?
CEMC Gauss (Grade 8), 2015
Pick one
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.
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