Let me give you a very broad clue to solving the problem. Think about using mathematical induction.
And while we are on the topic of mathematical induction, I thought I would post a recipe for Mandelbrot. Mandelbrots are the Jewish equivalent to biscotti. It is also, of course, the name of a very accomplished mathematician. Mandelbrots usually have almonds. Also, chocolate. They are great for an after-meal dessert. Anyway, here is the recipe.
Ingredients:
4 cups all-purpose flour
1 tablespoon baking powder
1 teaspoon salt
4 large eggs
1 1/3 cups sugar
3/4 cup vegetable oil
1 teaspoon vanilla extract
1/2 teaspoon almond extract (optional)
2 cups coarsely chopped almonds
Preparation:
Heat oven to 350 degrees. Line a large baking sheet with parchment paper.
In a large bowl, combine flour, baking powder and salt, and set aside. In another large bowl or stand mixer fitted with the whisk attachment, beat the eggs until well blended. Increase the speed to high and beat in the sugar 2 tablespoons at a time until mixture is thick and foamy, about 4 to 5 minutes.
Add oil and extract(s) to the eggs and beat briefly to blend. Replace whisk with the paddle attachment and, on lowest speed, beat in flour mixture and almonds just until mixture holds together. It will be soft, but shouldn't be too sticky. If necessary, add a few more tablespoons of flour.
Divide dough in half. Dampen hands lightly and form each half into a 3-inch-by-12-inch log on the prepared baking sheet, spacing 4 inches apart. Bake about 45 minutes or until golden brown and firm to the touch. Remove from oven and let cool at least 10 minutes.
Carefully place logs on a cutting board and cut diagonally with serrated knife or ham slicer into 1/2- to 3/4-inch slices.
Place pieces cut-side down on ungreased baking sheets. Bake 5 minutes. Turn pieces over and bake 5 minutes longer or until completely dry. Cool completely on wire racks. Store in an airtight container for up to 3 months or freeze.
