In a 7x7 grid, what is the number in the bottom right corner?

Question

My math teacher have presented me with a problem, that in my opinion is quite hard. It goes.

"You have a 7x7 grid. Some of the spaces in the grid are already filled with numbers. You have to insert numbers in the remaining spaces, so that the sum in every 3x3 grid inside the 7x7, is 2019. What number should be in the bottom right corner?" Here is the grid.

I know the answer is 7, but I have no idea of how you arrive at that answer.

Answer 1

Hint: fill in the sums in the boxes such that every 3x3 sub grid has the same sum. \begin{array}{|ccccc|} \hline 10 & \boxed{a+b} & 8 & \boxed{c+d} & 11 \\ \\ \\ 7 & \boxed{\phantom{0\quad 0}} & \boxed{\phantom 0} & \boxed{\phantom{0\quad 0}} & \boxed{\phantom 0} \\ \\ \\ 6 & \boxed{\phantom{0\quad 0}} & \boxed{\phantom 0} & \boxed{\phantom{0\quad 0}} & \boxed{\phantom 0} \\ \hline \end{array}