Consider the follow magic square highlighted in yellow. The sum of its rows and columns are in green and the sum of the diagonals in red. All of its sums are a square number with the sum of the whole square also being a square number.
The above square has a repeated sum in one each of the diagonal and one row and one column.
What is the smallest set numbers that you can put into a 3x3 grid so ALL 8 of its sums are all different square numbers and the sum of the whole also being a square number?
Using triangle numbers instead of square numbers 1, 3, 6, 10, 15, 21, 28, 36, 45,......... and so on What is the smallest set of number to result in all of its sums being triangle numbers with the sum of the whole also being a triangle number?