Infinite 3x3 Magic Square
Draft.
Work in Progress!
[This story is based on old recollections of what Arye Amitai told me over 35 years ago. While some details may be presented inaccurately, the specific mathematics details, which are of interest, are not.]
Sometime in the 1950's an Israeli periodical that was devoted to mathematics published a contest:
[I do not recall the precise text and rules of the contest and I don't know anyone who does.]
The standard true 3´ 3 magic square is









It uses the numbers 1 through 9 and all the rows, columns and two long diagonals add up to 15. Therefore, this magic square has 8 that equal 15.
A trivial solution for this contest is









It uses only the number 5 but in it any combination of three cells sums up to 15 for the grand total of 84 such sums. Since