Boldly Folding (part 2)

Geometry Level pending

There is a stack of \(n\) rectangular \(W \times L\) papers. You can use four different kinds of folds: \(\{up, down, left, right\}\)

  • \(up\) grabs all the layers from the bottom and folds it to the top.
  • \(down\) grabs all the layers from the top and folds it to the bottom.
  • \(left\) grabs all the layers from the right and folds it to the left.
  • \(right\) grabs all the layers from the left and folds it to the right.

After \(x\) 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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