Hi again Megan, one of my colleagues here on the Baker's Hotline (Linda) was kind and smart enough to be able to explain the math on this, so if you don't mind the rather long reply, here is her explanation:

The number of folds is a result of the type of folding (book fold vs. envelope) and how you count the layers. For a first ENVELOPE fold, you will have 9 layers i.e. (P=pastry and B = butter).

P

B

P

P

B

P

P

B

P

These seems like it should be 9 layers, but when counting we count it as 9-2 (we count the two adjacent pastry layers as 1). So 7 layers. For the next envelope fold, you would have 21-2 layers = 19. For the third fold, it is 19*3 or 57 layers, minus 2 = 55 layers. The last fold would give 55*3-2 layers, or 163.

For the second method, you start by using a BOOK fold. This is as follows:

P

B

P

P

B

P

P

B

P

P

B

P

We would count this as 12 layers - 3 = 9 layers (again because of the adjacent layers counted as one). Then with one envelope fold, you would have 9x3 layers - 2 = 25 layers.

I hope this helps!

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