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How to use a panmagic 4x4 square to produce a ‘most magic’ 4x4x4 cube?
The above mentioned 4x4x4 magic cube has the following magic features:
- the 4 rows, the 4 columns and the 2 diagonals in each level give the magic sum of 130:
- the 16 pillars give the magic sum of 130;
- the 16 diagonals (2x4 from the corners and 8x from the middle of the sides) through the 4 levels give the
magic sum of 130;
- The space diagonals give 100, 120, 140 respectively 160 instead of the magic sum of 130.
You can use a 4x4 panmagic square to produce a ‘nearly perfect’ magic 4x4x4 cube in the next five steps:
■ Transform a 4x4 panmagic square into the basic pattern of the 1st level of the 4x4x4 magic cube:
Panmagic 4x4 square -> Basic pattern 1st level
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1
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8
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10
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15
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8
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1
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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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13
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12
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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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11
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14
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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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2
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7
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16
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9
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■ Transform the basic pattern of the 1st level into the basic pattern of the 2nd level of the 4x4x4 magic cube:
Basic pattern 1st level -> Basic pattern 2nd level
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8
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1
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10
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15
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14
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11
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4
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5
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13
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12
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3
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6
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1
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8
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15
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10
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11
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14
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5
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4
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7
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2
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9
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16
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2
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7
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16
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9
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12
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13
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6
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3
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■ Produce the basic pattern of the 3rd level by diagonal (= vertical + horizontal) mirroring of the basic pattern of
the 2nd level of the 4x4x4 magic cube:
Basic pattern 2nd level -> Hor./vertical mirroring -> Basic pattern 3rd level
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14
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11
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4
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5
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12
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13
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6
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3
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3
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6
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13
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12
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1
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8
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15
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10
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7
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2
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9
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16
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16
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9
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2
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7
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7
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2
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9
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16
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1
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8
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15
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10
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10
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15
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8
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1
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12
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13
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6
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3
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14
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11
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4
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5
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5
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4
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11
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14
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■ Produce the basic pattern of the 4th level by diagonal (= vertical + horizontal) mirroring of the basic pattern of the
1st level of the 4x4x4 magic cube:
Basic pattern 1st level -> Hor./vertical mirroring -> Basic pattern 4th level
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8
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1
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10
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15
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2
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7
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16
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9
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9
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16
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7
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2
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13
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12
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3
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6
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11
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14
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5
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4
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4
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5
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14
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11
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11
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14
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5
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4
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13
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12
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3
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6
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6
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3
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12
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13
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2
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7
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16
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9
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8
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1
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10
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15
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15
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10
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1
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8
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■ Add in each level fixed column patterns to the basic patterns and produce the level by adding 1x digit from the basic
pattern to 16x the digit from the same cell of the column patern:
Basic pattern 1st level Column pattern 1st level 4x4x4 kube, 1st level
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8
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1
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10
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15
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3
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1
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2
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0
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56
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17
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42
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15
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13
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12
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3
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6
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1
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0
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3
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2
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29
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12
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51
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38
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11
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14
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5
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4
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2
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3
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0
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1
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43
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62
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5
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20
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2
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7
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16
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9
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0
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2
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1
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3
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2
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39
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32
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57
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Basic pattern 2nd level Column pattern 2nd level 4x4x4 cube, 2nd level
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14
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11
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4
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5
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1
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0
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3
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2
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30
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11
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52
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37
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1
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8
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15
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10
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0
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2
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1
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3
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1
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40
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31
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58
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7
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2
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9
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16
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3
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1
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2
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0
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55
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18
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41
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16
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12
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13
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6
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3
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2
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3
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0
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1
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44
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61
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6
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19
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Basic pattern 3rd level Column pattern 3rd level 4x4x4 cube, 3rd level
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3
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6
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13
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12
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2
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3
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0
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1
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35
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54
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13
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28
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16
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9
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2
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7
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3
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1
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2
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0
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64
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25
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34
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7
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10
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15
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8
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1
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0
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2
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1
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3
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10
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47
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24
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49
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5
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4
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11
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14
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1
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0
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3
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2
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21
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4
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59
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46
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Basic pattern 4th level Column pattern 4th level 4x4x4 cube, 4th level
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9
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16
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7
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2
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0
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2
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1
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3
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9
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48
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23
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50
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4
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5
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14
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11
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2
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3
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0
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1
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36
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53
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14
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27
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6
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3
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12
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13
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1
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0
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3
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2
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22
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3
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60
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45
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15
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10
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1
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8
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3
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1
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2
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0
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63
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26
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33
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8
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