I was just putting numbers on the paper and creating some patterns and while doing so, I noticed something.
1 2 3 4
2 4 1 3
3 1 4 2
4 3 2 1
This gives the value 10 if we sum the values horizontally or vertically or diagonally.
To make sure this also worked for other grid sizes I tried to use the same principle for a smaller grid size of 3x3 and a larger grid size of 5x5
1 2 3
2 2 2
3 2 1
I tried to apply the same principle for a 3x3 grid, summing the values horizontally, vertically gives the value 6, diagonally it doesn't seem to work but it seems to work for grids larger than 3x3 .
1 2 3 4 5
2 5 3 1 4
3 3 3 3 3
4 1 3 5 2
5 4 3 2 1
And using the same principle for a 5x5 grid and summing the values horizontally, vertically or diagonally gives the value 15.
It looks to be a bit different than the usual values we use in a magic square, and what I came up with has more of a pattern, especially when the grid is of uneven size.
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 2 5 3 1 4 2 5 3 1 4 2 5 3 1 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 1 3 5 2 4 1 3 5 2 4 1 3 5 2 5 4 3 2 1 5 4 3 2 1 5 4 3 2 1
Did I just create something completely new or is something like this already known in the mathematical world, if so what is it called?
Well, depending on how you arrange the numbers in the row, I'm not sure what principle you reside on but I'm noticing the pattern in the squares. The numbers you output by summing the diagonals/columns/rows are called triangular numbers and are of the form $$\frac{n(n+1)}{2}, \ \ n \in \mathbb{Z^+}$$ and notice that for $3 \times3$ squares it gives the output of $n=3$ and for $n \times n$ it gives $\frac{n(n+1)}{2}$, why? Simply because $$1+2+3+\dots+n=\frac{n(n+1)}{2}$$ So, I don't want to make you not excited, but it just may be an arrangement of the squares and the numbers in them that made such pattern manifest, so, sorry, but I don't think it would be a new thing in Math.