An exploration and extension of the old coursework favourite 'T Totals', the T-shape on a 9 x 9 grid, with an intention to identify the relationship between the T-number and the T-Total as the shape is translated about the grid.

What happens if we place the T-shape on a 7 x 7 grid? a 6 x 6 grid? a n x n grid?

How does this change for a 3 x 5 grid? a 5 x 3 grid? or a p x q grid?

What is the effect if we rotate or reflect the shape?