Upon seeing this drawing, I forgot the original problem and began to think if it was possible to fill the remaining cells with non-repeated numbers in such a way that the sum of the rows, columns and diagonals give the same sum, that is, form an almost square that be magical
After trying and trying I came to a solution.
And as always happens, one wants more, then I changed the black square of position and returned to look for a solution.
Once found the solutions, I thought if I could find solutions for 3 x 3 squares.
Here are the solutions found:
For 3x3 :
We see that only the middle one has all positive numbers
The magic sums of this almost square, magic are 9, 21 and 0 respectively.
For 4x4
In this case, all values are positive numbers.
and the magic sums are 56, 65 and 83 respectively
Some questions that came up:
a) For the 3x3 almost square, can you obtain almost squares with all positive numbers for all the models?
b) What is the smallest possible magic sum (using only positive numbers), for each model of almost square, 3x3 and 4x4?
