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# 4x4 Magic Squares

## Inventory with Colors

Rainbow

Fade

## Magic Carpet Squares

384 Carpet Squares
Carpet #1
Carpet #2
Carpet #3
(all)

from Carpet #2

from Carpet #3

## Links to Magic Square Sites

### Totals

0 | 1 | 14 | 15 |

11 | 13 | 2 | 4 |

12 | 6 | 9 | 3 |

7 | 10 | 5 | 8 |

Posted here are 7040 4x4 magic squares. These pages attempt to show the complete list of 4x4 magic squares.

Each square contains the numbers 0 thru 15, and each row, column, and diagonal should add up to 30. Any given square will have 7 other similar squares found by rotating and flipping. 7040/8=880.

The pages are arranged by the number that appears in the top left position of a square. At the top of each page are links that cause different color schemes to be applied. Below are examples of Odd/Even, Rainbow, and Fade.

Odd/Even0 | 1 | 14 | 15 |

11 | 13 | 2 | 4 |

12 | 6 | 9 | 3 |

7 | 10 | 5 | 8 |

0 | 1 | 14 | 15 |

11 | 13 | 2 | 4 |

12 | 6 | 9 | 3 |

7 | 10 | 5 | 8 |

0 | 1 | 14 | 15 |

11 | 13 | 2 | 4 |

12 | 6 | 9 | 3 |

7 | 10 | 5 | 8 |

Some 4x4 magic squares can be repeated to make a magic carpet. **There are 3 magic carpets** and each has these properties:

- Any 4x4 square contains the numbers 0-15.
- Any 4 squares in a horizontal line add up to 30.
- Any 4 squares in a vertical line add up to 30.
- Any 4 squares in a diagonal line add up to 30.
- Any 2x2 square adds up to 30.

Example squares from each of the 3 carpets:

from Carpet #10 | 7 | 9 | 14 |

11 | 12 | 2 | 5 |

6 | 1 | 15 | 8 |

13 | 10 | 4 | 3 |

0 | 7 | 10 | 13 |

11 | 12 | 1 | 6 |

5 | 2 | 15 | 8 |

14 | 9 | 4 | 3 |

0 | 7 | 12 | 11 |

13 | 10 | 1 | 6 |

3 | 4 | 15 | 8 |

14 | 9 | 2 | 5 |

These sites have more on the history and details of magic squares:

#in upper left | count | carpet squares |

0 | 416 | 24 |

1 | 400 | 24 |

2 | 404 | 24 |

3 | 476 | 24 |

4 | 432 | 24 |

5 | 456 | 24 |

6 | 460 | 24 |

7 | 476 | 24 |

8 | 476 | 24 |

9 | 460 | 24 |

10 | 456 | 24 |

11 | 432 | 24 |

12 | 476 | 24 |

13 | 404 | 24 |

14 | 400 | 24 |

15 | 416 | 24 |