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

Fade

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:

• Grogono
• Wikipedia
• Mathworld

Totals

#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