Can anyone guide me how to prove this question?

[omega16]

Can anyone guide me how to prove this question??

Question:
We want to describe via a picture a set of subsets of a square which are something like diagonals, but are not quite the same. We'll call them steep diagonals. One of them, labelled e, is illustrated in the square below; the other 6 are parallel to it

x_e_x_x_x_x_x
x_x_x_x_e_x_x
e_x_x_x_x_x_x
x_x_x_e_x_x_x
x_x_x_x_x_x_e
x_x_e_x_x_x_x
x_x_x_x_x_e_x

State and prove a theorem about under what conditions we can expect that the sums on the positive ( or negative ) steep diagonals are constant, when we're dealing with a square full of consecutive integers starting at 0.

 

[matt grime]

You're supposed to say what you've done before you get help.

 

[omega16]

Please guide me to start - a simple clue please , if possible. Thank you.
I really don't know what to start with for this question.

 

[matt grime]

Start by writing out the square, drawing some steep diagonals and then thinking about what you see.