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Excluding rotation and/or mirroring there are 880 different pure magic 4x4 squares. Of the 880 squares
48 are panmagic. These panmagic squares have (as well as the bigger [Franklin] panmagic squares) the
following pattern:
|
1
|
8
|
10
|
15
|
|
12
|
13
|
3
|
6
|
|
7
|
2
|
16
|
9
|
|
14
|
11
|
5
|
4
|
The sum of two digits of the same colour is each time (the highest digit of the magic square + 1, in this
case 16+1=) 17. For the patterns of all 880 pure magic 4x4 squares, go to: www.magic-squares.net/
transform.htm
You only need to know 3 panmagic squares to produce all (excluding rotation and/or mirroring) 48 panmagic
squares:
|
1
|
8
|
13
|
12
|
|
|
1
|
8
|
11
|
14
|
|
|
1
|
8
|
10
|
15
|
|
15
|
10
|
3
|
6
|
|
|
15
|
10
|
5
|
4
|
|
|
14
|
11
|
5
|
4
|
|
4
|
5
|
16
|
9
|
|
|
6
|
3
|
16
|
9
|
|
|
7
|
2
|
16
|
9
|
|
14
|
11
|
2
|
7
|
|
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12
|
13
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2
|
7
|
|
|
12
|
13
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3
|
6
|
On the 2x2 carpet of one of the three 4x4 squares you can find 16 different 4x4 sub-squares. See the following
example of the third square:
|
1
|
8
|
10
|
15
|
1
|
8
|
10
|
15
|
|
12
|
13
|
3
|
6
|
12
|
13
|
3
|
6
|
|
7
|
2
|
16
|
9
|
7
|
2
|
16
|
9
|
|
14
|
11
|
5
|
4
|
14
|
11
|
5
|
4
|
|
1
|
8
|
10
|
15
|
1
|
8
|
10
|
15
|
|
12
|
13
|
3
|
6
|
12
|
13
|
3
|
6
|
|
7
|
2
|
16
|
9
|
7
|
2
|
16
|
9
|
|
14
|
11
|
5
|
4
|
14
|
11
|
5
|
4
|
Select a random 4x4 sub-square on the carpet (stay out of the gray area, because of double solutions). The
(for example yellow marked) selected 4x4 sub-square can be rotated and/or mirrored (see below for what
happens to the digits):
|
Selected 4x4 square
|
4
|
14
|
11
|
5
|
|
Mirroring
|
|
5
|
11
|
14
|
4
|
|
|
|
|
|
|
15
|
1
|
8
|
10
|
|
|
|
10
|
8
|
1
|
15
|
|
|
|
|
|
|
6
|
12
|
13
|
3
|
|
|
|
3
|
13
|
12
|
6
|
|
|
|
|
|
|
9
|
7
|
2
|
16
|
|
|
|
16
|
2
|
7
|
9
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
A quarter turn
|
9
|
6
|
15
|
4
|
|
Mirroring
|
|
4
|
15
|
6
|
9
|
|
|
|
|
|
|
7
|
12
|
1
|
14
|
|
|
|
14
|
1
|
12
|
7
|
|
|
|
|
|
|
2
|
13
|
8
|
11
|
|
|
|
11
|
8
|
13
|
2
|
|
|
|
|
|
|
16
|
3
|
10
|
5
|
|
|
|
5
|
10
|
3
|
16
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
2x quarter turn
|
16
|
2
|
7
|
9
|
|
Mirroring
|
|
9
|
7
|
2
|
16
|
|
|
|
|
|
|
3
|
13
|
12
|
6
|
|
|
|
6
|
12
|
13
|
3
|
|
|
|
|
|
|
10
|
8
|
1
|
15
|
|
|
|
15
|
1
|
8
|
10
|
|
|
|
|
|
|
5
|
11
|
14
|
4
|
|
|
|
4
|
14
|
11
|
5
|
|
|
|
|
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|
3x quarter turn
|
5
|
10
|
3
|
16
|
|
Mirroring
|
|
16
|
3
|
10
|
5
|
|
|
|
|
|
|
11
|
8
|
13
|
2
|
|
|
|
2
|
13
|
8
|
11
|
|
|
|
|
|
|
14
|
1
|
12
|
7
|
|
|
|
7
|
12
|
1
|
14
|
|
|
|
|
|
|
4
|
15
|
6
|
9
|
|
|
|
9
|
6
|
15
|
4
|
There are 3 basic 4x4 panmagic squares. On the 2x2 carpet of one of the three 4x4 squares you can find 16
different 4x4 sub-squares (3x16=48). When you rotate and/or mirror one of the 48 different 4x4 squares, you
can find 8 different 4x4 squares. So 3 x 16 x 8 results in 384 different panmagic 4x4 squares (including rotation
and/or mirroring).
More information on page: Pan magic 4x4 square, explanation
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