How to produce 4x4 pan magic squares
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:
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1
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8
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10
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15
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12
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13
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3
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6
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7
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2
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16
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9
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14
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11
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5
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4
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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, got 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:
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1
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8
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13
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12
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1
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8
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11
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14
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1
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8
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10
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15
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15
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10
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3
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6
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15
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10
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5
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4
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14
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11
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5
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4
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4
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5
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16
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9
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6
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3
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16
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9
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7
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2
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16
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9
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14
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11
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2
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7
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12
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13
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2
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7
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12
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13
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3
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6
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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:
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1
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8
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10
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15
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1
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8
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10
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15
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12
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13
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3
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6
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12
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13
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3
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6
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7
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2
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16
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9
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7
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2
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16
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9
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14
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11
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5
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4
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14
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11
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5
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4
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1
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8
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10
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15
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1
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8
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10
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15
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12
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13
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3
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6
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12
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13
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3
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6
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7
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2
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16
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9
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7
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2
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16
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9
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14
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11
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5
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4
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14
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11
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5
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4
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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):
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Selected 4x4 square
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4
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14
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11
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5
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Mirroring
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5
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11
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14
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4
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15
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1
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8
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10
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10
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8
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1
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15
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6
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12
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13
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3
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3
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13
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12
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6
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9
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7
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2
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16
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16
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2
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7
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9
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A quarter turn
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9
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6
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15
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4
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Mirroring
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4
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15
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6
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9
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7
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12
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1
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14
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14
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1
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12
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7
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2
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13
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8
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11
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11
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8
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13
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2
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16
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3
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10
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5
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5
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10
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3
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16
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2x quarter turn
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16
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2
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7
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9
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Mirroring
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9
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7
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2
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16
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3
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13
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12
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6
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6
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12
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13
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3
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10
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8
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1
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15
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15
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1
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8
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10
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5
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11
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14
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4
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4
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14
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11
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5
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3x quarter turn
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5
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10
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3
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16
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Mirroring
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16
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3
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10
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5
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11
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8
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13
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2
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2
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13
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8
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11
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14
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1
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12
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7
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7
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12
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1
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14
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4
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15
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6
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9
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9
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6
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15
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4
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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" | 
