In this problem, due to the fact that the aim is to find the amount of ways in which a domino can be placed on a square board with any given dimensions; the amount of ways that the domino can be placed on the board is dependent upon the size, more importantly dimensions of the board. Therefore, the independent variable is the dimensions of the board (D), while the dependent variable is the number of ways that the domino can be placed on this board (N). Once again, it is important to note that each board has the dimensions of a square (all sides equal in length), while the domino has the dimensions of a rectangle (specifically 2 x 1 squares).
It is imperative that one develops and uses a system of counting the ways that a domino can be placed on a board, so as to assure that no positions of the domino on the board are missed or counted twice. As such I have counted and shown first, all the ways which the domino can be placed vertically in the top two rows (the domino, when placed vertically, will take up two rows and one column, because of the nature of the dimensions of the domino: 2 x 1), repeating this procedure for all rows, and then repeating that whole procedure with the domino placed horizontally, starting from the left column and finishing on the right:Derived from Norwegian and therefore traditionally of a Germanic origin, it was by the sword of the Norman conquest of 1066 and its bearers, speaking the language now known as old French, that William came to enter the English language. From the Norman Wilhelm: wil, meaning the will or desire; helm, meaning the helmet, or protection, its roots are inseparably tied with the history of the soldier. This connection is revealed even more openly in the Belgian translation Guildhelm, meaning “harnessed with a gilded helmet". After the Norman conquest and during the middle ages, the name William grew as the most popular name in England, owing largely to the historic figures of the time who bore it: most notably...