December 22, 2024

Magic Square Formula

This is a formula I discovered around 3 or 4 years back on how to make a 3×3 magic square such that all numbers in the square are different from each other. The formula goes –

Let the column numbers be c1, c2, c3, and rows are r1, r2, and r3. Let us take a base number as n. then the numbers we need to input to get the magic square is –

(Note:- the column numbers go from left to right and row numbers go from up to down.)

  1. R1 c1 = n
  2. R2 c2 = 2n
  3. R1 c3 = 3n
  4. R1 c1 = 2n-1
  5. R3 c3 = 2n+1
  6. R1 c2 = n+1
  7. R2 c1 = 3n+1
  8. R3 c2 = 3n-1
  9. R2 c3 = n-1
    It must be noted that we need to take base n >= 3 otherwise numbers will be repeated.

Also, columns and rows can be shifted to make the square look more complicated.

R1 c1 and r3 c3 can be interchanged and the changes in the others can be made accordingly.