How to produce a 9x9 pan magic square?
I don’t know how many pure (pan)magic 9x9 squares exist.
A 9x9 panmagic square can be produced using a method of construction which is comparable with the method to
produce a 5x5 panmagic square (see also on this website).
Fill in the first row of the 1st square: 0, 1, 2, 3, 4, 5, 6, 7 and 8. Produce the second and third row of the 1st square
by moving the digits each time 3 places to the left.
1 st square, first three rows
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0
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1
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8
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8
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0
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8
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0
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8
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0
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8
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0
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7
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8
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The first three rows of the 1st square consist of three 3x3 sub-squares. Produce the second three rows of the 1st
square by switching the sequence of the three columns of the three 3x3 sub-squares to 2-3-1. Produce the second
three rows of the 1st square by switching the sequence of the three columns of the three 3x3 sub-squares to 3-1-2.
1 st square
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0
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1
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2
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3
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5
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7
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8
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6
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7
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8
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0
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1
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6
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7
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8
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0
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1
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2
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3
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4
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5
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1
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2
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0
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4
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5
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3
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7
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8
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6
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4
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5
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3
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7
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8
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6
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1
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2
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0
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7
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8
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6
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1
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2
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0
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4
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5
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3
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2
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0
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1
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5
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3
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4
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8
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6
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7
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5
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3
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4
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8
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6
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7
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2
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0
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1
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8
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6
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7
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2
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0
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1
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5
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3
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4
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Produce the 2nd square by rotating the 1st square (a quarter turn to the right). Take a digit from the 1st square multi-
plied by 9 and add (1x) the digit from the same cell of the 2nd square.
9x digit + 1x digit = panmagic 9x9 square
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0
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1
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2
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3
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4
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5
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6
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7
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8
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8
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5
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2
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7
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4
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1
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6
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3
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0
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8
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14
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20
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34
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40
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46
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60
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66
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72
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3
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4
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5
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6
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7
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8
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0
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1
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2
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6
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3
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0
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8
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5
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2
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7
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4
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1
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33
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39
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45
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62
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68
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74
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7
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13
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19
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6
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7
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8
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0
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1
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2
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3
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4
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5
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7
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4
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1
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6
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3
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0
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8
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5
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2
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61
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67
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73
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6
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12
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18
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35
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41
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47
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1
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2
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0
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4
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5
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3
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7
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8
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6
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2
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8
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5
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1
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7
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4
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0
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6
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3
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11
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26
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5
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37
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52
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31
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63
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78
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57
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4
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5
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3
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7
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8
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6
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1
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2
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0
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0
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6
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3
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2
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8
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5
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1
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7
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4
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36
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51
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30
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65
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80
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59
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10
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25
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4
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7
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8
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6
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1
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2
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0
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4
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5
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3
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1
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7
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4
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0
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6
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3
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2
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8
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5
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64
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79
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58
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9
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24
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3
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38
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53
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32
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2
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0
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1
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5
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3
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4
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8
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6
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7
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5
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2
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8
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4
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1
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7
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3
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0
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6
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23
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2
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17
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49
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28
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43
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75
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54
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69
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5
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3
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4
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8
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6
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7
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2
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0
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1
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3
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0
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6
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5
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2
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8
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4
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1
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7
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48
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27
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42
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77
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56
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71
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22
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1
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16
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8
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6
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7
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2
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0
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1
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5
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3
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4
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4
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1
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7
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3
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0
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6
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5
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2
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8
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76
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55
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70
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21
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0
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15
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50
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29
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44
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In the square consists of the digits 0 up to 80. By adding 1 to each digit you can produce a square which cionsists of the
digits 1 up to 81.
You can use this method to produce squares which have the size of odd number squared (= 9x9, 25x25, 49x49, 81x81,
121x121, ...). For example, to produce a 25x25 square use the digits 0 up to 24 as first row of the 1st square. Produce
the second up to fifth row of the 1st square by moving the digits each time 5 places to the left. Produce the second up to
fifth five rows (= 5x5 sub-squares) of the 1st square by switching the sequence of the five columns of the five 5x5 sub-
squares to 2-3-4-5-1, 3-4-5-1-2, 4-5-1-2-3 respectively 5-1-2-3-4. | 
