Use the problem analysis and design components and techniques that we discussed in class, including problem decomposition and stepwise refinement, to develop a list of generalized detailed instructions (in English) for determining (by hand) the product of any two 2-digit natural numbers (e.g., 99 x 99). (The instructions must work for any and all sets of two 2-digit numbers, not only for a specific pair you choose.) Assume that the recipient of your instructions only knows how to multiply two single-digit numbers (up to 9 x 9), add two single-digit numbers (up to 9 + 9), and can access the digits of a multi-digit number.

In your written solution, discuss the overall and intermediate goals, outputs, inputs, assumptions, available tools, and how you broke down the problem into simpler components. Include an example problem and solution (e.g. long-hand multiplication) to help illustrate your analysis and approach. Also provide a detailed step-through of the logic of your instructions for at least the following different test cases (99 x 99, 1x1, 86 x 23), to help discover and correct errors in your instructions.