Interactive Magic Square
Drag numbers or click cells to arrange them
Validation
The Legend
According to Chinese mythology, around 2200 BCE, the Yellow River flooded repeatedly. Emperor Yu tried to channel the waters, but failed until he saw a magical turtle emerge from the Luo River. On its shell was a perfect 3×3 pattern of dots where every row, column, and diagonal summed to 15. This pattern, called Lo Shu, became the foundation of Chinese numerology and influenced feng shui principles for millennia.
The Mathematics
Magic Square: An n×n grid where each row, column, and main diagonal sum to the same magic constant.
For 3×3: Magic constant = n(n²+1)/2 = 3(9+1)/2 = 15
Lo Shu: The unique 3×3 magic square with numbers 1-9 (up to rotations and reflections). There are 8 orientations total (4 rotations × 2 reflections).
Pattern: Odd numbers occupy corners and center; even numbers occupy edge midpoints. The center is always 5 (the median).
Properties
• Each row, column, and diagonal sums to 15
• Uses each digit 1-9 exactly once
• Displays 2-fold rotational symmetry
• Complementary pairs opposite the center (5) sum to 10