How to Play Magic Squares

Magic Squares is a classic mathematical puzzle where you arrange numbers in a square grid so that every row, column, and main diagonal sums to the same "Magic Constant."

Rules

1. Grid Size: Choose n (typically 3×3, 4×4, 5×5).
2. Number Set: Use consecutive integers 1 to n² (e.g., 1–9 for 3×3).
3. Placement: Fill each cell with a unique number.
4. Validation: All rows, columns, and both diagonals must equal the Magic Constant.

Magic Constant Formula

M = n(n² + 1) / 2

• 3×3: M = 3(9+1)/2 = 15
• 4×4: M = 4(16+1)/2 = 34

Example: Solved 3×3 (Lo Shu Square)

 | 8 | 1 | 6 | = 15
 | 3 | 5 | 7 | = 15
 | 4 | 9 | 2 | = 15 

Columns: 8+3+4=15, 1+5+9=15, 6+7+2=15. Diagonals: 8+5+2=15, 6+5+4=15.

Solving Tips (Odd-Order Squares: Siamese Method)

1. Place 1 in the middle of the top row.
2. Move up one row, right one column for the next number.
3. If move exits grid: wrap around (top↔bottom, left↔right).
4. If cell is occupied: move down one row from last filled cell instead.
5. Repeat until grid is full.

Even-order squares (4×4, 6×6) require different algorithms (e.g., Strachey, LUX).