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Introduction to Magic Squares
The sum of the numbers on each row, column, and two main diagonals is equal
Magic squares are ancient mathematical puzzles full of charm. Below is a detailed introduction:
1. What is a Magic Square?
A Magic Square is an n×n square matrix composed of distinct numbers that satisfies:
- The sum of numbers in each row and column is equal
- The sum of numbers in both main diagonals is also equal
- Typically uses consecutive natural numbers from 1 to n² (some variations may allow repeated numbers)
2. Key Concepts
Magic Constant
The common sum of each row/column/diagonal. Calculation formula:
`Magic Constant = n(n² + 1)/2`
- 3×3 Magic Square: Magic Constant = 15
- 4×4 Magic Square: Magic Constant = 34
Classification by Order
1. Odd-order(e.g., 3×3, 5×5)
2. Doubly even-order(4×4, 8×8, i.e., multiples of 4)
3. Singly even-order(6×6, 10×10, i.e., even numbers not multiples of 4)
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