Boldly Folding (part 2)
There is a stack of
rectangular
papers. You can use four different kinds of folds:
- grabs all the layers from the bottom and folds it to the top.
- grabs all the layers from the top and folds it to the bottom.
- grabs all the layers from the right and folds it to the left.
- grabs all the layers from the left and folds it to the right.
After folds, how many layers exist?
Details and assumptions:
- The papers have infinitesimal thickness.
- All of the papers in the stack are aligned with one another.
House turtle folded by Herng Yi .
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1 solution
If you don't fold at all, your number of layers is n .
If you fold once, your number of layers doubles: n 2 .
If you fold twice, your number of layers doubles again: n ⋅ 2 ⋅ 2 .
If you fold three times, your number of layers doubles again: n ⋅ 2 ⋅ 2 ⋅ 2 .
We can start to see a trend; The number of layers after x folds is n 2 x .