magic square is an arrangement of numbers from $1$ to n$2$ in an $[$n x n$]$ matrix, with each

number occurring exactly once, and such that the sum of the entries of any row, any column,

or any main diagonal is the same. One method of generating a magic square in cases where n

is odd is as follows: Place a $1$ in any cell $($in the centre cell of the top row, for example$),$ then

place subsequent numbers by moving one cell above and to the right. The counting is wrapped

around, so that falling off the top returns on the bottom and falling off the right returns on the

left. When a cell is encountered which is already filled, the next number is instead placed in

the cell below the previous one and the method continues as before.

An example of a magic square is shown in Listing $1.$

Provide all the source code necessary for modelling the generation of a magic square.

A partial class diagram is given in Figure $1.$ You must use this in your solution but you may

add additional functions and data members as required. You may also create additional classes

as needed. Emphasis should be placed in demonstrating your understanding of the design

patterns that you learned about during the cours