Here's a recap of Hilton's four steps:$1.$ Solve an instance by hand. Be creative and brainstorm about how to approach the puzzle.a$.$ Keep track of the questions you ask and how you answer them.b$.$ What decisions do you have to make? What are your options?c$.$ Do you ever have to back up$?$ How do you know? How far back do you go$?$d$.$ What steps do you have to repeat? How many times? Is the number of repetitionsalways the same or does it depend on something else?$2.$ Write down what you did$$not the solution, but the steps you took to find the solution$($that is$,$ the algorithm$).$ Write a list of clear steps that someone else could follow and getthe same answer$\mathrm{.}3.$ Generalize your steps. What parts are details of this specific puzzle? What parts would bethe same for other instances of this puzzle? What parts would be different?$4.$ Test your algorithm. Once you ha