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Magic Square Calculator 4x4

Magic Square Rules:

Arrange numbers 1 to 16 in a 4×4 grid so that the sum of numbers in each row, each column, and both main diagonals equals 34.

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1. What is a 4×4 Magic Square?

A 4×4 magic square is a grid containing the numbers 1 to 16 arranged so that the sum of numbers in each row, each column, and both main diagonals equals the same value (34 for 4×4 squares).

2. How Does the Magic Square Work?

The magic square follows these rules:

  • Contains numbers 1 to 16 exactly once each
  • All rows sum to 34
  • All columns sum to 34
  • Both main diagonals sum to 34

Explanation: The magic constant (34) is calculated as n(n²+1)/2 where n=4 (size of square).

3. Properties of 4×4 Magic Squares

Details: There are 880 distinct 4×4 magic squares. They have additional properties like quadrant sums and center sums that also equal 34 in many cases.

4. Using the Calculator

Tips: Click "Generate New Square" to create a different valid 4×4 magic square. The magic constant will always be 34.

5. Frequently Asked Questions (FAQ)

Q1: How many 4×4 magic squares exist?
A: There are 880 distinct normal 4×4 magic squares (not counting rotations/reflections).

Q2: Can magic squares be larger than 4×4?
A: Yes, magic squares can be any size, though the complexity increases with size.

Q3: What's the history of magic squares?
A: Magic squares date back to ancient China (650 BCE) and were later studied by Arab and European mathematicians.

Q4: Are there other types of magic squares?
A: Yes, including panmagic squares (all diagonals including broken ones sum to constant), and associative squares (numbers symmetric to center sum to n²+1).

Q5: What are magic squares used for?
A: Besides mathematical interest, they've been used in art, cryptography, and even as good luck charms in some cultures.

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