Editing Magic square (section)

===Medjig-method for squares of even order 2''n'', where ''n'' > 2===
In this method a magic square is "multiplied" with a medjig square to create a larger magic square. The namesake of this method derives from mathematical game called medjig created by Willem Barink in 2006, although the method itself is much older.{{citation needed|date=September 2022}} An early instance of a magic square constructed using this method occurs in Yang Hui's text for order 6 magic square.{{citation needed|date=September 2022}} The [[LUX method]] to construct singly even magic squares is a special case of the medjig method, where only 3 out of 24 patterns are used to construct the medjig square.{{citation needed|date=September 2022}}

The pieces of the medjig puzzle are 2×2 squares on which the numbers 0, 1, 2 and 3 are placed. There are three basic patterns by which the numbers 0, 1, 2 and 3 can be placed in a 2×2 square, where 0 is at the top left corner:

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{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:4em;height:4em;table-layout:fixed;"
|-
| 0 || 1 
|-
| 2 || 3 
|}
{{col-break|valign=bottom|gap=3em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:4em;height:4em;table-layout:fixed;"
|-
| 0 || 1 
|-
| 3 || 2 
|}
{{col-break|valign=bottom|gap=3em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:4em;height:4em;table-layout:fixed;"
|-
| 0 || 2 
|-
| 3 || 1 
|}
{{col-end}}

Each pattern can be reflected and rotated to obtain 8 equivalent patterns, giving us a total of 3×8 = 24 patterns. The aim of the puzzle is to take ''n''<sup>2</sup> medjig pieces and arrange them in an ''n'' × ''n'' ''medjig square'' in such a way that each row, column, along with the two long diagonals, formed by the medjig square sums to 3''n'', the magic constant of the medjig square. An ''n'' × ''n'' medjig square can create a 2''n'' × 2''n'' magic square where ''n'' > 2.

Given an ''n''×''n'' medjig square and an ''n''×''n'' magic square base, a magic square of order 2''n''×2''n'' can be constructed as follows:
* Each cell of an ''n''×''n'' magic square is associated with a corresponding 2×2 subsquare of the medjig square
* Fill each 2×2 subsquares of the medjig square with the four numbers from 1 to 4''n''<sup>2</sup> that equal the original number modulo ''n''<sup>2</sup>, i.e. ''x''+''n''<sup>2</sup>''y'' where ''x'' is the corresponding number from the magic square and ''y'' is a number from 0 to 3 in the 2×2 subsquares.

Assuming that we have an initial magic square base, the challenge lies in constructing a medjig square. For reference, the sums of each medjig piece along the rows, columns and diagonals, denoted in italics, are:

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{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:8em;height:6em;table-layout:fixed;"
|-
| style="border-right:solid"| ''1'' || style="border-top:solid"| 0 || style="border-right:solid;border-top:solid"| 1 
|-
| style="border-right:solid"| ''5'' || 2 || style="border-right:solid"| 3 
|-
| ''3'' || style="border-top:solid"| ''2'' || style="border-top:solid"|''4'' || ''3'' 
|}
{{col-break|valign=bottom|gap=3em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:8em;height:6em;table-layout:fixed;"
|-
| style="border-right:solid"| ''1'' || style="border-top:solid"| 0 || style="border-right:solid;border-top:solid"| 1 
|-
| style="border-right:solid"| ''5'' ||3 || style="border-right:solid"| 2 
|-
| ''4'' || style="border-top:solid"| ''3'' || style="border-top:solid"| ''3'' || ''2''
|}
{{col-break|valign=bottom|gap=3em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:8em;height:6em;table-layout:fixed;"
|-
| style="border-right:solid"| ''2'' || style="border-top:solid"| 0 || style="border-right:solid;border-top:solid"| 2 
|-
| style="border-right:solid"| ''4'' || 3 || style="border-right:solid"| 1 
|-
| ''5'' || style="border-top:solid"| ''3'' || style="border-top:solid"| ''3'' || ''1''
|}
{{col-end}}

'''Doubly even squares''': The smallest even ordered medjig square is of order 2 with magic constant 6. While it is possible to construct a 2×2 medjig square, we cannot construct a 4×4 magic square from it since 2×2 magic squares required to "multiply" it does not exist. Nevertheless, it is worth constructing these 2×2 medjig squares. The magic constant 6 can be partitioned into two parts in three ways as 6 = 5 + 1 = 4 + 2 = 3 + 3. There exist 96 such 2×2 medjig squares.{{citation needed|date=September 2022}} In the examples below, each 2×2 medjig square is made by combining different orientations of a single medjig piece.

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{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:8em;height:8em;table-layout:fixed;"
|-
|+ Medjig 2×2
|-
| 0 || style="border-right:solid"|1 || 3 || 2
|-
| 2 || style="border-right:solid"|3 || 1 || 0
|-
| style="border-top:solid"|3 || style="border-top:solid;border-right:solid"|2 || style="border-top:solid"|0 || style="border-top:solid"|1 
|- 
| 1 || style="border-right:solid"|0 || 2 || 3
|}
{{col-break|valign=bottom|gap=3em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:8em;height:8em;table-layout:fixed;"
|-
|+ Medjig 2×2
|-
| 0 || style="border-right:solid"|1 || 2 || 3
|-
| 3 || style="border-right:solid"|2 || 1 || 0
|-
| style="border-top:solid"|1 || style="border-top:solid;border-right:solid"|0 || style="border-top:solid"|3 || style="border-top:solid"|2
|-
| 2 || style="border-right:solid"|3 || 0 || 1
|}
{{col-break|valign=bottom|gap=3em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:8em;height:8em;table-layout:fixed;"
|-
|+ Medjig 2×2
|-
| 0 || style="border-right:solid"|2 || 3 || 1 
|-
| 3 || style="border-right:solid"|1 || 0 || 2
|-
| style="border-top:solid"|0 || style="border-top:solid;border-right:solid"|2 || style="border-top:solid"|3 || style="border-top:solid"|1
|-
| 3 || style="border-right:solid"|1 || 0 || 2
|}
{{col-end}}

We can use the 2×2 medjig squares to construct larger even ordered medjig squares. One possible approach is to simply combine the 2×2 medjig squares together. Another possibility is to wrap a smaller medjig square core with a medjig border. The pieces of a 2×2 medjig square can form the corner pieces of the border. Yet another possibility is to append a row and a column to an odd ordered medjig square. An example of an 8×8 magic square is constructed below by combining four copies of the left most 2×2 medjig square given above:

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{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:8em;height:8em;table-layout:fixed;"
|-
|+ Order 4
|-
| 1 || 14 || 4 || 15
|-
| 8 || 11 || 5 || 10
|-
| 13 || 2 || 16 || 3
|-
| 12 || 7 || 9 || 6
|}
{{col-break|valign=bottom|gap=1em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:16em;height:16em;table-layout:fixed;"
|-
|+ Medjig 4 × 4
|-
| 0 || style="border-right:solid"| 1 || 3 || style="border-right:solid"|2 || 0 || style="border-right:solid"|1 || 3 || 2
|-
| 2 || style="border-right:solid"|3 || 1 || style="border-right:solid"|0 || 2 || style="border-right:solid"|3 || 1 || 0
|-
| style="border-top:solid"|3 || style="border-right:solid; border-top:solid"|2 || style="border-top:solid"|0 || style="border-right:solid; border-top:solid"|1 || style="border-top:solid"|3 || style="border-top:solid; border-right:solid"|2 || style="border-top:solid"|0 || style="border-top:solid"|1
|-
| 1 || style="border-right:solid"|0 || 2 || style="border-right:solid"|3 || 1 || style="border-right:solid"|0 ||2 || 3
|-
| style="border-top:solid"|0 || style="border-right:solid; border-top:solid "|1 || style="border-top:solid"|3 || style="border-right:solid; border-top:solid"|2 || style="border-top:solid"|0 || style="border-top:solid; border-right:solid"|1 || style="border-top:solid"|3 || style="border-top:solid"|2 
|-
| 2 || style="border-right:solid"|3 || 1 || style="border-right:solid"|0 || 2 || style="border-right:solid"|3 || 1 || 0
|-
| style="border-top:solid"|3 || style="border-right:solid; border-top:solid "|2 || style="border-top:solid"|0 || style="border-right:solid; border-top:solid"|1 || style="border-top:solid"|3 || style="border-top:solid; border-right:solid"|2 || style="border-top:solid"|0 || style="border-top:solid"|1
|-
| 1 || style="border-right:solid"|0 || 2 || style="border-right:solid"|3 || 1 || style="border-right:solid"|0 || 2 || 3
|}
{{col-break|valign=bottom|gap=1em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:16em;height:16em;table-layout:fixed;"
|-
|+ Order 8
|-
| '''1''' || style="border-right:solid"| 17 || 62 || style="border-right:solid"| 46 || '''4''' || style="border-right:solid"|20 || 63 || 47
|-
| 33 || style="border-right:solid"| 49 || 30 || style="border-right:solid"| '''14''' || 36 || style="border-right:solid"|52 || 31 || '''15'''
|-
| style="border-top:solid"| 56 || style="border-right:solid; border-top:solid"| 40 || style="border-top:solid"| '''11''' || style="border-right:solid; border-top:solid"| 27 || style="border-top:solid"| 53 || style="border-top:solid; border-right:solid"| 37 || style="border-top:solid"|'''10''' || style="border-top:solid"|26
|-
| 24 || style="border-right:solid"| '''8''' || 43 || style="border-right:solid"| 59 || 21 || style="border-right:solid"|'''5''' || 42 || 58
|-
| style="border-top:solid"| '''13''' || style="border-right:solid; border-top:solid "| 29 || style="border-top:solid"| 50 || style="border-right:solid; border-top:solid"| 34 || style="border-top:solid"| '''16''' || style="border-top:solid; border-right:solid"| 32 || style="border-top:solid"|51 || style="border-top:solid"|35
|-
| 45 || style="border-right:solid"| 61 || 18 || style="border-right:solid"| '''2''' || 48 || style="border-right:solid"|64 || 19 || '''3'''
|-
| style="border-top:solid"| 60 || style="border-right:solid; border-top:solid "| 44 || style="border-top:solid"| '''7''' || style="border-right:solid; border-top:solid"| 23 || style="border-top:solid"| 57 || style="border-top:solid; border-right:solid"| 41 || style="border-top:solid"| '''6''' || style="border-top:solid"|22
|-
| 28 || style="border-right:solid"| '''12''' || 39 || style="border-right:solid"| 55 || 25 || style="border-right:solid"|'''9''' || 38 || 54
|}
{{col-end}}

The next example is constructed by bordering a 2×2 medjig square core.

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{{col-break|valign=bottom}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:8em;height:8em;table-layout:fixed;"
|-
|+ Order 4
|-
| 1 || 14 || 4 || 15
|-
| 8 || 11 || 5 || 10
|-
| 13 || 2 || 16 || 3
|-
| 12 || 7 || 9 || 6
|}
{{col-break|valign=bottom|gap=1em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:16em;height:16em;table-layout:fixed;"
|-
|+ Medjig 4 × 4
|-
| 0 || style="border-right:solid"| 1 || 0 || style="border-right:solid"|1 || 2 || style="border-right:solid"|3 || 3 || 2
|-
| 2 || style="border-right:solid"|3 || 3 || style="border-right:solid"|2 || 1 || style="border-right:solid"|0 || 1 || 0
|-
| style="border-top:solid"|0 || style="border-right:solid; border-top:solid"|3 || style="border-top:solid"|0 || style="border-right:solid; border-top:solid"|2 || style="border-top:solid"|3 || style="border-top:solid; border-right:solid"|1 || style="border-top:solid"|0 || style="border-top:solid"|3
|-
| 1 || style="border-right:solid"|2 || 3 || style="border-right:solid"|1 || 0 || style="border-right:solid"|2 ||1 || 2
|-
| style="border-top:solid"|2 || style="border-right:solid; border-top:solid "|1 || style="border-top:solid"|0 || style="border-right:solid; border-top:solid"|2 || style="border-top:solid"|3 || style="border-top:solid; border-right:solid"|1 || style="border-top:solid"|2 || style="border-top:solid"|1 
|-
| 3 || style="border-right:solid"|0 || 3 || style="border-right:solid"|1 || 0 || style="border-right:solid"|2 || 3 || 0
|-
| style="border-top:solid"|3 || style="border-right:solid; border-top:solid "|2 || style="border-top:solid"|0 || style="border-right:solid; border-top:solid"|1 || style="border-top:solid"|2 || style="border-top:solid; border-right:solid"|3 || style="border-top:solid"|0 || style="border-top:solid"|1
|-
| 1 || style="border-right:solid"|0 || 3 || style="border-right:solid"|2 || 1 || style="border-right:solid"|0 || 2 || 3
|}
{{col-break|valign=bottom|gap=1em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:16em;height:16em;table-layout:fixed;"
|-
|+ Order 8
|-
| '''1''' || style="border-right:solid"| 17 || '''14''' || style="border-right:solid"| 30 || 36 || style="border-right:solid"|52 || 63 || 47
|-
| 33 || style="border-right:solid"| 49 || 62 || style="border-right:solid"| 46 || 20 || style="border-right:solid"|'''4''' || 31 || '''15'''
|-
| style="border-top:solid"| '''8''' || style="border-right:solid; border-top:solid"| 56 || style="border-top:solid"| '''11''' || style="border-right:solid; border-top:solid"| 43 || style="border-top:solid"| 53 || style="border-top:solid; border-right:solid"| 21 || style="border-top:solid"|'''10''' || style="border-top:solid"| 58
|-
| 24 || style="border-right:solid"| 40 || 59 || style="border-right:solid"| 27 || '''5''' || style="border-right:solid"|37 || 26 || 42
|-
| style="border-top:solid"| 45 || style="border-right:solid; border-top:solid "| 29 || style="border-top:solid"| '''2''' || style="border-right:solid; border-top:solid"| 34 || style="border-top:solid"| 64 || style="border-top:solid; border-right:solid"| 32 || style="border-top:solid"| 35 || style="border-top:solid"|19
|-
| 61 || style="border-right:solid"| '''13''' || 50 || style="border-right:solid"| 18 || '''16''' || style="border-right:solid"|48 || 51 || '''3'''
|-
| style="border-top:solid"| 60 || style="border-right:solid; border-top:solid "| 44 || style="border-top:solid"| '''7''' || style="border-right:solid; border-top:solid"| 23 || style="border-top:solid"| 41 || style="border-top:solid; border-right:solid"| 57 || style="border-top:solid"| '''6''' || style="border-top:solid"|22
|-
| 28 || style="border-right:solid"| '''12''' || 55 || style="border-right:solid"| 39 || 25 || style="border-right:solid"|'''9''' || 38 || 54
|}
{{col-end}}

'''Singly even squares''': Medjig square of order 1 does not exist. As such, the smallest odd ordered medjig square is of order 3, with magic constant 9. There are only 7 ways of partitioning the integer 9, our magic constant, into three parts.{{citation needed|date=September 2022}} If these three parts correspond to three of the medjig pieces in a row, column or diagonal, then the relevant partitions for us are:

: 9 = 1 + 3 + 5 = 1 + 4 + 4 = 2 + 3 + 4 = 2 + 2 + 5 = 3 + 3 + 3.

A 3×3 medjig square can be constructed with some trial-and-error, as in the left most square below. Another approach is to add a row and a column to a 2×2 medjig square. In the middle square below, a left column and bottom row has been added, creating an L-shaped medjig border, to a 2×2 medjig square given previously. The right most square below is essentially same as the middle square, except that the row and column has been added in the middle to form a cross while the pieces of 2×2 medjig square are placed at the corners.

{{col-begin|width=auto;margin:0.5em auto}}
{{col-break|valign=bottom}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:12em;height:12em;table-layout:fixed;"
|-
|+ Medjig 3 × 3
|-
| 2 || style="border-right:solid"| 3 || 0 || style="border-right:solid"|2 || 0 || 2
|-
| 1 || style="border-right:solid"|0 || 3 || style="border-right:solid"|1 || 3 || 1
|-
| style="border-top:solid"|3 || style="border-right:solid; border-top:solid"|1 || style="border-top:solid"|1 || style="border-right:solid; border-top:solid"|2 || style="border-top:solid"|2 || style="border-top:solid"|0
|-
| 0 || style="border-right:solid"|2 || 0 || style="border-right:solid"|3 || 3 || 1
|-
| style="border-top:solid"|3 || style="border-right:solid; border-top:solid "|2 || style="border-top:solid"|2 || style="border-right:solid; border-top:solid"|0 || style="border-top:solid"|0 || style="border-top:solid"|2
|-
| 0 || style="border-right:solid"|1 || 3 || style="border-right:solid"|1 || 1 || 3
|}
{{col-break|valign=bottom|gap=1em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:12em;height:12em;table-layout:fixed;"
|-
|+ Medjig 3 × 3
|-
| 0 || style="border-right:solid"| 3 || 0 || style="border-right:solid"|1 || 3 || 2
|-
| 2 || style="border-right:solid"|1 || 2 || style="border-right:solid"|3 || 1 || 0
|-
| style="border-top:solid"|3 || style="border-right:solid; border-top:solid"|0 || style="border-top:solid"|3 || style="border-right:solid; border-top:solid"|2 || style="border-top:solid"|0 || style="border-top:solid"|1
|-
| 2 || style="border-right:solid"|1 || 1 || style="border-right:solid"|0 || 2 || 3
|-
| style="border-top:solid"|0 || style="border-right:solid; border-top:solid "|1 || style="border-top:solid"|3 || style="border-right:solid; border-top:solid"|1 || style="border-top:solid"|3 || style="border-top:solid"|1
|-
| 2 || style="border-right:solid"|3 || 0 || style="border-right:solid"|2 || 0 || 2
|}
{{col-break|valign=bottom|gap=1em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:12em;height:12em;table-layout:fixed;"
|-
|+ Medjig 3 × 3
|-
| 0 || style="border-right:solid"| 1 || 0 || style="border-right:solid"|3 || 3 || 2
|-
| 2 || style="border-right:solid"|3 || 2 || style="border-right:solid"|1 || 1 || 0
|-
| style="border-top:solid"|3 || style="border-right:solid; border-top:solid"|1 || style="border-top:solid"|0 || style="border-right:solid; border-top:solid"|1 || style="border-top:solid"|3 || style="border-top:solid"|1
|-
| 0 || style="border-right:solid"|2 || 2 || style="border-right:solid"|3 || 0 || 2
|-
| style="border-top:solid"|3 || style="border-right:solid; border-top:solid "|2 || style="border-top:solid"|3 || style="border-right:solid; border-top:solid"|0 || style="border-top:solid"|0 || style="border-top:solid"|1
|-
| 1 || style="border-right:solid"|0 || 2 || style="border-right:solid"|1 || 2 || 3
|}
{{col-end}}

Once a 3×3 medjig square has been constructed, it can be converted into a 6×6 magic square. For example, using the left most 3×3 medjig square given above:

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{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:6em;height:6em;table-layout:fixed;"
|-
|+ Order 3
|-
| 8 || 1 || 6
|-
| 3 || 5 || 7
|-
| 4 || 9 || 2
|}
{{col-break|valign=bottom|gap=1em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:12em;height:12em;table-layout:fixed;"
|-
|+ Medjig 3 × 3
|-
| 2 || style="border-right:solid"| 3 || 0 || style="border-right:solid"|2 || 0 || 2
|-
| 1 || style="border-right:solid"|0 || 3 || style="border-right:solid"|1 || 3 || 1
|-
| style="border-top:solid"|3 || style="border-right:solid; border-top:solid"|1 || style="border-top:solid"|1 || style="border-right:solid; border-top:solid"|2 || style="border-top:solid"|2 || style="border-top:solid"|0
|-
| 0 || style="border-right:solid"|2 || 0 || style="border-right:solid"|3 || 3 || 1
|-
| style="border-top:solid"|3 || style="border-right:solid; border-top:solid "|2 || style="border-top:solid"|2 || style="border-right:solid; border-top:solid"|0 || style="border-top:solid"|0 || style="border-top:solid"|2
|-
| 0 || style="border-right:solid"|1 || 3 || style="border-right:solid"|1 || 1 || 3
|}
{{col-break|valign=bottom|gap=1em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:12em;height:12em;table-layout:fixed;"
|-
|+ Order 6
|-
| 26 || style="border-right:solid"| 35 || '''1''' || style="border-right:solid"| 19 || '''6''' || 24
|-
| 17 || style="border-right:solid"| '''8''' || 28 || style="border-right:solid"| 10 || 33 || 15
|-
| style="border-top:solid"| 30 || style="border-right:solid; border-top:solid"| 12 || style="border-top:solid"| 14 || style="border-right:solid; border-top:solid"| 23 || style="border-top:solid"| 25 || style="border-top:solid"| '''7'''
|-
| '''3''' || style="border-right:solid"| 21 || '''5''' || style="border-right:solid"| 32 || 34 || 16
|-
| style="border-top:solid"| 31 || style="border-right:solid; border-top:solid "| 22 || style="border-top:solid"| 27 || style="border-right:solid; border-top:solid"| '''9''' || style="border-top:solid"| '''2''' || style="border-top:solid"| 20
|-
| '''4''' || style="border-right:solid"| 13 || 36 || style="border-right:solid"| 18 || 11 || 29
|}
{{col-end}}

There are 1,740,800 such 3×3 medjig squares.<ref>http://budshaw.ca/2xNComposite.html, 2N Composite Squares, S. Harry White, 2009</ref> An easy approach to construct higher order odd medjig square is by wrapping a smaller odd ordered medjig square with a medjig border, just as with even ordered medjig squares. Another approach is to append a row and a column to an even ordered medjig square. Approaches such as the LUX method can also be used. In the example below, a 5×5 medjig square is created by wrapping a medjig border around a 3×3 medjig square given previously:

{{col-begin|width=auto;margin:0.5em auto}}
{{col-break|valign=bottom}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:10em;height:10em;table-layout:fixed;"
|-
|+ Order 5
|-
| 17 || 24 || 1 || 8 || 15
|-
| 23 || 5 || 7 || 14 || 16
|-
| 4 || 6 || 13 || 20 || 22
|-
| 10 || 12 || 19 || 21 || 3
|-
| 11 || 18 || 25 || 2 || 9 
|}
{{col-break|valign=bottom|gap=1em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:20em;height:20em;table-layout:fixed;"
|-
|+ Medjig 5 × 5
|-
| 0 || style="border-right:solid"| 1 || 3 || style="border-right:solid"|1 || 0 || style="border-right:solid"|1 || 3 || style="border-right:solid"|1 || 3 || 2
|-
| 2 || style="border-right:solid"|3 || 0 || style="border-right:solid"|2 || 2 || style="border-right:solid"|3 || 0 || style="border-right:solid"|2 || 1 || 0
|-
| style="border-top:solid"|3 || style="border-right:solid; border-top:solid"|0 || style="border-top:solid"|2 || style="border-right:solid; border-top:solid"|3 || style="border-top:solid"|0 || style="border-right:solid; border-top:solid"|2 || style="border-top:solid"|0 || style="border-right:solid; border-top:solid"|2 || style="border-top:solid"|1 || style="border-top:solid"|2
|-
| 1 || style="border-right:solid"|2 || 1 || style="border-right:solid"|0 || 3 || style="border-right:solid"|1 || 3 || style="border-right:solid"|1 || 3 || 0
|-
| style="border-top:solid"|0 || style="border-right:solid; border-top:solid"|2 || style="border-top:solid"|3 || style="border-right:solid; border-top:solid"|1 || style="border-top:solid"|1 || style="border-right:solid; border-top:solid"|2 || style="border-top:solid"|2 || style="border-right:solid; border-top:solid"|0 || style="border-top:solid"|1 || style="border-top:solid"|3
|-
| 1 || style="border-right:solid"|3 || 0 || style="border-right:solid"|2 || 0 || style="border-right:solid"|3 || 3 || style="border-right:solid"|1 || 0 || 2 
|-
| style="border-top:solid"|3 || style="border-right:solid; border-top:solid"|0 || style="border-top:solid"|3 || style="border-right:solid; border-top:solid"|2 || style="border-top:solid"|2 || style="border-right:solid; border-top:solid"|0 || style="border-top:solid"|0 || style="border-right:solid; border-top:solid"|2 || style="border-top:solid"|1 || style="border-top:solid"|2
|-
| 1 || style="border-right:solid"|2 || 0 || style="border-right:solid"|1 || 3 || style="border-right:solid"|1 || 1 || style="border-right:solid"|3 || 3 || 0
|-
| style="border-top:solid"|3 || style="border-right:solid; border-top:solid"|2 || style="border-top:solid"|1 || style="border-right:solid; border-top:solid"|3 || style="border-top:solid"|1 || style="border-right:solid; border-top:solid "|0 || style="border-top:solid"|1 || style="border-right:solid; border-top:solid"|3 || style="border-top:solid"|0 || style="border-top:solid"|1
|-
| 1 || style="border-right:solid"|0 || 2 || style="border-right:solid"|0 || 3 || style="border-right:solid"|2 || 2 || style="border-right:solid"|0 || 2 || 3 
|}
{{col-break|valign=bottom|gap=1em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:20em;height:20em;table-layout:fixed;"
|-
|+ Order 10
|-
| '''17''' || style="border-right:solid"| 42 || 99 || style="border-right:solid"| 49 || '''1''' || style="border-right:solid"|26 || 83 || style="border-right:solid"|33 || 90 || 65
|-
| 67 || style="border-right:solid"| 92 || '''24''' || style="border-right:solid"| 74 || 51 || style="border-right:solid"|76 || '''8''' || style="border-right:solid"|58 || 40 || '''15'''
|-
| style="border-top:solid"| 98 || style="border-right:solid; border-top:solid"| '''23''' || style="border-top:solid"| 55 || style="border-right:solid; border-top:solid"| 80 || style="border-top:solid"| '''7''' || style="border-right:solid; border-top:solid"| 57 || style="border-top:solid"| '''14''' || style="border-right:solid; border-top:solid"| 64 || style="border-top:solid"| 41 || style="border-top:solid"| 66
|-
| 48 || style="border-right:solid"| 73 || 30 || style="border-right:solid"| '''5''' || 82 || style="border-right:solid"| 32 || 89 || style="border-right:solid"| 39 || 91 || '''16'''
|-
| style="border-top:solid"| '''4''' || style="border-right:solid; border-top:solid "| 54 || style="border-top:solid"| 81 || style="border-right:solid; border-top:solid"| 31 || style="border-top:solid"| 38 || style="border-right:solid; border-top:solid"| 63 || style="border-top:solid"| 70 || style="border-right:solid; border-top:solid"| '''20''' || style="border-top:solid"| 47 || style="border-top:solid"| 97
|-
| 29 || style="border-right:solid"| 79 || '''6''' || style="border-right:solid"| 56 || '''13''' || style="border-right:solid"| 88 || 95 || style="border-right:solid"| 45 || '''22''' || 72
|-
| style="border-top:solid"| 85 || style="border-right:solid; border-top:solid"| '''10''' || style="border-top:solid"| 87 || style="border-right:solid; border-top:solid"| 62 || style="border-top:solid"| 69 || style="border-right:solid; border-top:solid"| '''19''' || style="border-top:solid"| '''21''' || style="border-right:solid; border-top:solid"| 71 || style="border-top:solid"| 28 || style="border-top:solid"| 53
|-
| 35 || style="border-right:solid"| 60 || '''12''' || style="border-right:solid"| 37 || 94 || style="border-right:solid"| 44 || 46 || style="border-right:solid"| 96 || 78 || '''3'''
|-
| style="border-top:solid"| 86 || style="border-right:solid; border-top:solid "| 61 || style="border-top:solid"| 43 || style="border-right:solid; border-top:solid"| 93 || style="border-top:solid"| 100 || style="border-right:solid; border-top:solid"| '''25''' || style="border-top:solid"| 27 || style="border-right:solid; border-top:solid"| 77 || style="border-top:solid"| '''9''' || style="border-top:solid"| 34
|-
| 36 || style="border-right:solid"| '''11''' || 68 || style="border-right:solid"| '''18''' || 95 || style="border-right:solid"| 75 || 52|| style="border-right:solid"| '''2''' || 59 || 84
|}
{{col-end}}