Toothpicks

Part 1 - Two dimensional (not too bad)

You are to determine a function T(L, W) that gives the number of toothpicks required to build a rectangular grid with length L and width W. For example:

Part 2 - Three dimensional (much harder)

You are to determine a function T(L, W, H) that gives the number of toothpicks required to build a 3-D grid of length L, width W, and height H. For example:

Requirements and Hints

You must hand in your functions along with a clear explanation of where those functions came from and/or why they work. Simplify your functions as much as possible (Multiply out everything and combine all like terms). You should try your functions on a variety of other grids to verify that they do work.

For part 1, think in terms of rows and columns. How is the number of rows related to the length of the grid? How many toothpicks are in each row? How is the number of columns related to the width of the grid? How many toothpicks are in each column?

For part 2, think in terms of floors and pillars. How is the number of floors related to the height of the grid? How many toothpicks are in each floor? How many rows and columns of pillars are there? How is the number of pillars related to the length and width of the grid?