*n**

*n*grid as follows:

The grid must then be filled with the integers 1 through

*n*, while adhering to the following rules:

- Boxes with matching x and y coordinates (box (a,a), box (b,b), etc.) must be filled with the integer "1". (The diagonal from the top left to the bottom right is filled with all 1s.)
- If box (m,n) is filled with a certain integer, box (n,m) must be filled with the same integer. (The entries are symmetrical across the diagonal of 1s.)
- No single row or column may contain two of the same integer.

One such valid solution is as follows:

The following questions are to be answered or solved:

- Prove that if an n * n grid has a solution, then one of its solutions has the first row of boxes filled with the integers 1 through n in ascending order from left to right.
- Find a generalized algorithm for producing a single solution to an n * n grid where n is even, or prove that at least one solution exists for all such n.
- Find a generalized algorithm for producing a single solution to an n * n grid where n is odd, or prove that no solutions exist for all such n.
- Find the number of unique solutions for each n > 0.

I have part 1 solved, but I have no idea where to go after that. How should I go about attacking this problem, SEN?

None.