|
Office Applications and Entertainment, Magic Squares of Subtraction
|
|
Attachment 4.1 |
About the Author
|
Order 4 Magic Squares of Subtraction, Group 1 (Complete)
Res4 = 4, Pair Sum = 17
1
| 12 |
15 |
10 |
13 |
| 9 |
14 |
11 |
16 |
| 7 |
4 |
5 |
2 |
| 6 |
1 |
8 |
3 |
|
2
| 5 |
15 |
7 |
13 |
| 8 |
14 |
6 |
16 |
| 10 |
4 |
12 |
2 |
| 11 |
1 |
9 |
3 |
|
3
| 11 |
16 |
9 |
14 |
| 10 |
13 |
12 |
15 |
| 8 |
3 |
6 |
1 |
| 5 |
2 |
7 |
4 |
|
4
| 6 |
16 |
8 |
14 |
| 7 |
13 |
5 |
15 |
| 9 |
3 |
11 |
1 |
| 12 |
2 |
10 |
4 |
|
Res4 = 6, Pair Sum = 17
5
| 13 |
11 |
7 |
15 |
| 8 |
16 |
12 |
14 |
| 10 |
2 |
4 |
6 |
| 5 |
3 |
9 |
1 |
|
6
| 13 |
3 |
7 |
15 |
| 8 |
16 |
12 |
6 |
| 10 |
2 |
4 |
14 |
| 5 |
11 |
9 |
1 |
|
7
| 12 |
14 |
8 |
16 |
| 7 |
15 |
13 |
11 |
| 9 |
1 |
5 |
3 |
| 4 |
6 |
10 |
2 |
|
8
| 12 |
6 |
8 |
16 |
| 7 |
15 |
13 |
3 |
| 9 |
1 |
5 |
11 |
| 4 |
14 |
10 |
2 |
|
9
| 10 |
2 |
6 |
12 |
| 3 |
13 |
9 |
1 |
| 11 |
5 |
7 |
15 |
| 8 |
16 |
14 |
4 |
|
10
| 7 |
15 |
14 |
12 |
| 11 |
13 |
8 |
16 |
| 3 |
5 |
10 |
2 |
| 9 |
1 |
6 |
4 |
|
11
| 9 |
1 |
3 |
13 |
| 6 |
12 |
10 |
2 |
| 14 |
4 |
8 |
16 |
| 7 |
15 |
11 |
5 |
|
12
| 8 |
16 |
11 |
13 |
| 14 |
12 |
7 |
15 |
| 6 |
4 |
9 |
1 |
| 10 |
2 |
3 |
5 |
|
Order 4 Magic Squares of Subtraction, Group 2 (Crosswise Symmetric)
Res4 = 4, Pair Sum = 17
|
|
|
|
1
| 12 |
10 |
15 |
13 |
| 7 |
5 |
4 |
2 |
| 9 |
11 |
14 |
16 |
| 6 |
8 |
1 |
3 |
|
2
| 5 |
7 |
15 |
13 |
| 10 |
12 |
4 |
2 |
| 8 |
6 |
14 |
16 |
| 11 |
9 |
1 |
3 |
|
3
| 11 |
9 |
16 |
14 |
| 8 |
6 |
3 |
1 |
| 10 |
12 |
13 |
15 |
| 5 |
7 |
2 |
4 |
|
4
| 6 |
8 |
16 |
14 |
| 9 |
11 |
3 |
1 |
| 7 |
5 |
13 |
15 |
| 12 |
10 |
2 |
4 |
|
Res4 = 6, Pair Sum = 17
5
| 13 |
7 |
11 |
15 |
| 10 |
4 |
2 |
6 |
| 8 |
12 |
16 |
14 |
| 5 |
9 |
3 |
1 |
|
6
| 13 |
7 |
3 |
15 |
| 10 |
4 |
2 |
14 |
| 8 |
12 |
16 |
6 |
| 5 |
9 |
11 |
1 |
|
7
| 12 |
8 |
14 |
16 |
| 9 |
5 |
1 |
3 |
| 7 |
13 |
15 |
11 |
| 4 |
10 |
6 |
2 |
|
8
| 12 |
8 |
6 |
16 |
| 9 |
5 |
1 |
11 |
| 7 |
13 |
15 |
3 |
| 4 |
10 |
14 |
2 |
|
9
| 10 |
6 |
2 |
12 |
| 11 |
7 |
5 |
15 |
| 3 |
9 |
13 |
1 |
| 8 |
14 |
16 |
4 |
|
10
| 7 |
14 |
15 |
12 |
| 3 |
10 |
5 |
2 |
| 11 |
8 |
13 |
16 |
| 9 |
6 |
1 |
4 |
|
11
| 9 |
3 |
1 |
13 |
| 14 |
8 |
4 |
16 |
| 6 |
10 |
12 |
2 |
| 7 |
11 |
15 |
5 |
|
12
| 8 |
11 |
16 |
13 |
| 6 |
9 |
4 |
1 |
| 14 |
7 |
12 |
15 |
| 10 |
3 |
2 |
5 |
|
Order 4 Magic Squares of Subtraction, Group 3 (Associated)
Res4 = 8, Pair Sum = 17
1
| 16 |
7 |
14 |
13 |
| 11 |
12 |
9 |
2 |
| 15 |
8 |
5 |
6 |
| 4 |
3 |
10 |
1 |
|
2
| 16 |
6 |
15 |
13 |
| 10 |
12 |
9 |
3 |
| 14 |
8 |
5 |
7 |
| 4 |
2 |
11 |
1 |
|
3
| 16 |
15 |
6 |
13 |
| 14 |
5 |
8 |
7 |
| 10 |
9 |
12 |
3 |
| 4 |
11 |
2 |
1 |
|
4
| 16 |
14 |
7 |
13 |
| 15 |
5 |
8 |
6 |
| 11 |
9 |
12 |
2 |
| 4 |
10 |
3 |
1 |
|
5
| 12 |
11 |
2 |
9 |
| 7 |
16 |
13 |
14 |
| 3 |
4 |
1 |
10 |
| 8 |
15 |
6 |
5 |
|
6
| 12 |
10 |
3 |
9 |
| 6 |
16 |
13 |
15 |
| 2 |
4 |
1 |
11 |
| 8 |
14 |
7 |
5 |
|
7
| 12 |
3 |
10 |
9 |
| 2 |
1 |
4 |
11 |
| 6 |
13 |
16 |
15 |
| 8 |
7 |
14 |
5 |
|
8
| 12 |
2 |
11 |
9 |
| 3 |
1 |
4 |
10 |
| 7 |
13 |
16 |
14 |
| 8 |
6 |
15 |
5 |
|
Order 4 Magic Squares of Subtraction, Group 6 (Axial Symmetric)
Res4 = 4, Pair Sum = 17
|
|
|
|
1
| 12 |
15 |
9 |
14 |
| 10 |
13 |
11 |
16 |
| 7 |
4 |
6 |
1 |
| 5 |
2 |
8 |
3 |
|
2
| 5 |
15 |
8 |
14 |
| 7 |
13 |
6 |
16 |
| 10 |
4 |
11 |
1 |
| 12 |
2 |
9 |
3 |
|
3
| 12 |
9 |
15 |
14 |
| 7 |
6 |
4 |
1 |
| 10 |
11 |
13 |
16 |
| 5 |
8 |
2 |
3 |
|
4
| 5 |
8 |
15 |
14 |
| 10 |
11 |
4 |
1 |
| 7 |
6 |
13 |
16 |
| 12 |
9 |
2 |
3 |
|
5
| 11 |
16 |
10 |
13 |
| 9 |
14 |
12 |
15 |
| 8 |
3 |
5 |
2 |
| 6 |
1 |
7 |
4 |
|
6
| 6 |
16 |
7 |
13 |
| 8 |
14 |
5 |
15 |
| 9 |
3 |
12 |
2 |
| 11 |
1 |
10 |
4 |
|
7
| 11 |
10 |
16 |
13 |
| 8 |
5 |
3 |
2 |
| 9 |
12 |
14 |
15 |
| 6 |
7 |
1 |
4 |
|
8
| 6 |
7 |
16 |
13 |
| 9 |
12 |
3 |
2 |
| 8 |
5 |
14 |
15 |
| 11 |
10 |
1 |
4 |
|
Order 4 Magic Squares of Subtraction, Group 11 (Mixed Symmetry)
Res4 = 6, Pair Sum = 17
|
|
|
|
1
| 7 |
14 |
12 |
11 |
| 10 |
6 |
5 |
3 |
| 13 |
16 |
8 |
15 |
| 4 |
2 |
9 |
1 |
|
2
| 12 |
14 |
7 |
11 |
| 5 |
6 |
10 |
3 |
| 8 |
16 |
13 |
15 |
| 9 |
2 |
4 |
1 |
|
3
| 13 |
15 |
8 |
16 |
| 4 |
1 |
9 |
2 |
| 7 |
11 |
12 |
14 |
| 10 |
3 |
5 |
6 |
|
|
Order 4 Magic Squares of Subtraction, Group 12 (Mixed Symmetry)
Res4 = 6, Pair Sum = 17
|
|
|
|
1
| 7 |
12 |
14 |
11 |
| 13 |
8 |
16 |
15 |
| 10 |
5 |
6 |
3 |
| 4 |
9 |
2 |
1 |
|
2
| 12 |
7 |
14 |
11 |
| 8 |
13 |
16 |
15 |
| 5 |
10 |
6 |
3 |
| 9 |
4 |
2 |
1 |
|
3
| 13 |
8 |
15 |
16 |
| 7 |
12 |
11 |
14 |
| 4 |
9 |
1 |
2 |
| 10 |
5 |
3 |
6 |
|
|