4x4 Magic Squares
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
#1
 0 1 14 15 11 13 2 4 12 6 9 3 7 10 5 8

# 4x4 Magic Squares

## Inventory with Colors

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/Even
 0 1 14 15 11 13 2 4 12 6 9 3 7 10 5 8
Rainbow
 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

## Magic Carpet Squares

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

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 #1
 0 7 9 14 11 12 2 5 6 1 15 8 13 10 4 3
from Carpet #2
 0 7 10 13 11 12 1 6 5 2 15 8 14 9 4 3
from Carpet #3
 0 7 12 11 13 10 1 6 3 4 15 8 14 9 2 5

## Links to Magic Square Sites

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

### Totals

 #in upper left count carpetsquares 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