# Field Farming System

# Field Farming System

Ching-Tang Tseng

Hamilton, New Zealand

16 June 2018

ilikeforth@gmail.com

http://forthfornight.blogspot.com

Before 361 BC, the agricultural policy in whole China were dominated by a so called  # field farming system. According to the Chinese historical record, a former prime minister Shang Yang (商鞅390 - 338 BC) of The Chin Dynasty (秦朝221-207 BC) scrapped such a system. Over those olden societies, land belongs to emperor, without private farm. Farming land in one unit was partitioned into nine square parts, the same as a # (pronouncing: sharp) mark. Surround the center of #, eight family farmers cultivated eight farms. They should cultivate the central farm conjointly as well. After annual harvest session, central farm production belongs to the emperor.  Extra tax of those eight family farmers will be calculated out based on the production of central farm. Tax of the higher harvest family pays more. For example, tax rate will be 10% of the over amount. Tax of the lower harvest family pays nothing.

In spite of # field farming system had been scrapped, before 361 BC were the peaceful era especially applauded by Confucius (孔子551~479 BC). Peaceful level described by Chinese is: people were lived in the days of spring and autumn (春秋時期). No war, no robber king, no killer emperor in that period of time.

# field farming system had ever been operated in a period of peaceful days, in memory of it, this article described a FORTH code able to apply to # field farming system. Regardless the answer of whether this system was nice or not? Obviously, history told us, annual tax rate to be set to “Between 10% to 15%” was a make sense range. It was a worth yearning value. Politician’s behavior makes tax rate higher.

The following FORTH code will be written in Chinese on purpose. This is another kind of application to use FORTH. I don’t like any FORTH system that is disabled in using Chinese. Coding ABC FORTH in any kind of language is possible. Chinese display function was supported by operating system. I did nothing. Code feature shows that I am able to use only 11 BASIC style instructions to solve all kinds of mathematical problem. Their corresponding Chinese names are listing as following:

1. LET  計算

2. FOR  就從

3. TO     做到

4. STEP  間隔

5. NEXT  配合

6. GOTO  跳到

7. IF         假如

8. THEN  前往

9.  RUN   執行

10. PRINT   印出

11. END     結束

You are welcome to trace back to all posted articles in this blog. All BASIC style codes inside adopted these 11 instructions only. That means only one instruction to be used in each line. Executing speed of one BASIC instruction is the same as one FORTH word.

11 special Chinese names were consolidated down after deeply thinking. On the meaning aspect, they are fully matched. On the grammar aspect, they are fully accordant to Chinese language. On the future development aspect, two syllables pronunciation let these instructions apt to distinct in speech identification.

Code and its execution outcomes:

\ 井田制度下的稅收

\ 日期：2018-06-14

\ 作者：曾慶潭於紐西蘭

\ 使用系統: Ubuntu 16.04, Lina64

3 3 浮點矩陣 井田    

3 3 浮點矩陣 稅額

2 個浮點變數 稅率 稅量

2 個整數變數 列號 行號

: 輸入收成

 {{ 井田 ( 1 1 ) = 8230.0 e 0 }} {{ 井田 ( 1 2 ) = 7930.0 e 0 }} {{ 井田 ( 1 3 ) = 6300.0 e 0 }}

 {{ 井田 ( 2 1 ) = 6970.0 e 0 }} {{ 井田 ( 2 2 ) = 7560.0 e 0 }} {{ 井田 ( 2 3 ) = 7900.0 e 0 }}

 {{ 井田 ( 3 1 ) = 8050.0 e 0 }} {{ 井田 ( 3 2 ) = 7800.0 e 0 }} {{ 井田 ( 3 3 ) = 8010.0 e 0 }}

;

: 稅額歸零     

  中文程式

10 就從   列號 = 1 做到 3

20 就從   行號 = 1 做到 3

30 計算   { 稅額 ( 列號 行號 ) = 0.0 e 0 }

40 配合 行號

50 配合 列號

60 執行 輸入收成

70 計算  { 稅率 = 0.1 e 0 }

80 結束

;

: 稅收     

  中文程式

10 執行 稅額歸零

20 就從 列號 = 1 做到 3

30 就從 行號 = 1 做到 3

40 假如 { 井田 ( 列號  行號 ) <= 井田 ( 2 2 ) } 前往 70

50 計算 { 稅額 ( 列號  行號 ) = ( 井田 ( 列號 行號 ) - 井田 ( 2 2 ) ) * 稅率 }

60 跳到 80

70 計算 { 稅額 ( 列號  行號 ) = 0.0 e 0 }

80 計算 { 稅量 = 稅額 ( 列號  行號 ) }

90 印出  " 井田( " ; 列號 ; 行號 ; " )的稅額為: "

100 執行 稅量 f. ." 斤稻穀 " cr

110 配合 行號

120 配合 列號

130 結束 ;

: main 稅收 ;

\S

ching@center:~$ cd lina64

ching@center:~/lina64$ ./f

AMDX86 ciforth 5.2.1

fload field

Loading OK above \S

 OK

main

井田( 1 1 )的稅額為:  67.0斤稻穀

井田( 1 2 )的稅額為:  37.0斤稻穀

井田( 1 3 )的稅額為:  0.0斤稻穀

井田( 2 1 )的稅額為:  0.0斤稻穀

井田( 2 2 )的稅額為:  0.0斤稻穀

井田( 2 3 )的稅額為:  34.0斤稻穀

井田( 3 1 )的稅額為:  49.0斤稻穀

井田( 3 2 )的稅額為:  24.0斤稻穀

井田( 3 3 )的稅額為:  45.0斤稻穀

 OK

My personal testing remarks: Chinese coding ability approved.

反擊不良媒體，個人永久自衛貼文

這是一篇硬遭無禮媒體臉書刪文的訊息，本人不客氣回應臉書，本人不刪就是不刪。

臉書不准貼文，那麼，我就在我的個人網頁上專貼此文永久紀念，給臉書永久的難看。

美國朋友來信標題為：咎由自取！

此份文件係好友來信，發件自美國，此姓名地址欄故意略去。 2017年6月21日 上午4:01
收件者: Ching-Tang Tseng <ilikeforth@gmail.com>
【轉載】
『巴拿馬總統
    記者會...』

記者：總統先生請問為何要與中華民國斷交？

總統：從107年前還是清朝年代時，我們就與中國建立了良好的邦誼，直到現在也並未改變。

記者：未改變？那這次斷交怎麼解釋？

總統：當年我們建交的是中國，就是民主革命成功的中華民國，並不是台灣國。
但是去年中華民國總統來訪時，我們發現他們的這個總統簽字時，署名為「台灣總統」。並不是我們所原先建交的中國(中華民國)，所以才跟他們台灣斷交，跟中國政府建交。


Ching-Tang Tseng <ilikeforth@gmail.com>
2017年6月21日 上午7:46
寄給 <姓名略去>


讚！

One set answer of magic square matrix

One set answer of magic square matrix

曾慶潭 Ching-Tang Tseng

ilikeforth@gmail.com

Hamilton, New Zealand

2 June 2018

兩千六百年前，中國的信史記載，古人這樣表示、研究、應用魔術方陣。

兩千六百年後的今天，中國人這樣子表示、研究、應用魔術方陣。

\ magic square matrics generator
\ Author: Ching-Tang Tseng
\ 20150528, Hamilton, New Zealand

\ ******************************
\ (1).Data structure declared heap

\ Attention! max is a reserved word of mathematical function.
10 integers x y l n q sqd2 q2 nr maxx msum
100 100 (matrix) sq

\ ***********************************
\ (2).Data input heap

: 4n+2init
  basic
\ 10 let n = 6
20 let msum = n * ( n ** 2 + 1 ) / 2
30 let sqd2 = n / 2 :: q2 = sqd2 ** 2
40 let l = ( n - 2 ) / 4
50 let x = sqd2 / 2 + 1 :: y = 1
60 let nr = 1
70 end ;

: 2n+1init
  basic
\ 10 let n = 7
20 let nr = 1
30 let x = n - ( n / 2 )
40 let y = 1
50 let msum = n * ( n ** 2 + 1 ) / 2
50 let maxx = n * n
60 end ;

: 4ninit
  basic
\ 10 let n = 8
20 let msum = n * ( n ** 2 + 1 ) / 2
30 let q = n / 4
40 let nr = 1
50 end ;

\ ********************************
\ (3).Auxiliary instructions heap

: check-columms-and-rows
  basic
10 For y = 1 To n
20 let nr = 0 :: q = 0
30 For x = 1 To n
40 let nr = nr + sq ( x y )
50 let q = q + sq ( y x )
60 Next x
70 If nr <> msum Or q <> msum Then 90
80 goto 100
90 run cr x 4  .r y 4 .r cr -1 abort" Error1: value <> magic sum " cr
100 Next y
110 end ;

: check-diagonals
  basic
10 let nr = 0 :: q = 0
20 For x = 1 To n
30 let nr = nr + sq ( x  x )
40 let q = q + sq ( x  ( n - x + 1 ) )
50 Next x
60 If nr <> msum Or q <> msum Then 80
70 goto 90
80 run cr nr . 3 spaces q . 3 spaces cr -1 abort" Error2: value <> magic sum " cr
90 end ;

: EraseSq
  basic
10 for y = 1 to 100
20 for x = 1 to 100
30 let sq ( x y ) = 0
40 next x
50 next y
60 end ;

: PrintSq
  basic
10 Print " Magic square size : " ; n ; " * " ; n
20 Print " The magic sum = " ; msum
30 run cr
40 For y = 1 To n
50 For x = 1 To n
60 let q = sq ( x y )
70 run q 4 .R
80 Next x
90 run cr
100 Next y
110 end ;

\ *******************************
\ (4).Main code heap

: 2n+1
  basic
10 if sq ( x y ) = 0 then 30
20 goto 100
30 let sq ( x y ) = nr

40 if nr mod n = 0 then 70
50 let x = x + 1
55 let y = y - 1
60 goto 80
70 let y = y + 1

80 let nr = nr + 1

100 if x > n then 120
110 goto 200
120 let x = 1
130 if sq ( x y ) <> 0 then 150
140 goto 200
150 let x = x + 1

200 if y < 1 then 220
210 goto 300
220 let y = n
230 if sq ( x y ) <> 0 then 250
240 goto 300
250 let y = y - 1

300 if nr > maxx then 400
310 goto -10

400 end ;

: 4n
  basic
10 for y = 1 to n
20 for x = q + 1 to n - q
30 let sq ( x y ) = 1
40 next x
50 next y
60 For x = 1 To n
70 For y = q + 1 To n - q
80 let sq ( x y ) = sq ( x y ) xor 1
90 Next y
100 Next x

110 let q = n * n + 1
120 for y = 1 To n
130 for x = 1 To n
140 if sq ( x y ) = 0 Then 170
150 let sq ( x y ) = nr
160 goto 180
170 let sq ( x y ) = q - nr
180 let nr = nr + 1
190 Next x
200 Next y
210 end ;

\ Attention! in ABC FORTH, index can not be an algebraic expression
: x+sqd2 x sqd2 + ;
: y+sqd2 y sqd2 + ;
: l+1 l 1+ ;

: 4n+2
  basic
10 if sq ( x y ) = 0 then 30
20 goto 130
30 let sq ( x y ) = nr
40 let sq ( x+sqd2 y+sqd2 ) = nr + q2
50 let sq ( x+sqd2 y ) = nr + q2 * 2
60 let sq ( x y+sqd2 ) = nr + q2 * 3

70 if nr mod sqd2 = 0 then 90
80 goto 110
90 let y = y + 1
100 goto 120
110 let x = x + 1 :: y = y - 1
120 let nr = nr + 1

130 if x > sqd2 then 150
140 goto 200
150 let x = 1
160 if sq ( x y ) <> 0 then 180
170 goto 200
180 let x = x + 1

200 if y < 1 then 220
210 goto 260
220 let y = sqd2
230 if sq ( x y ) <> 0 then 250
240 goto 260
250 let y = y - 1

260 if nr > q2 then 300
270 goto -10

300 for y = 1 to sqd2
310 for x = 1 to l
320 let q = sq ( x y )
330 let sq ( x y ) = sq ( x y+sqd2 )
340 let sq ( x y+sqd2 ) = q
350 next x
360 next y

400 let y = ( sqd2 / 2 ) + 1
410 let q = sq ( 1 y )
420 let sq ( 1 y ) = sq ( 1 y+sqd2 )
430 let sq ( 1 y+sqd2 ) = q
440 let q = sq ( l+1 y )
450 let sq ( l+1 y ) = sq ( l+1 y+sqd2 )
460 let sq ( l+1 y+sqd2 ) = q

500 for y = 1 to sqd2
510 for x = n - l + 2 to n
520 let q = sq ( x y )
530 let sq ( x y ) = sq ( x y+sqd2 )
540 let sq ( x y+sqd2 ) = q
550 next x
560 next y

1000 end ;

\ **********************
\ (5).Manipulation heap

: magics ( n -- )
  [[ n ]] !
  EraseSq
  basic
10 if n mod 2 = 1 then 100
20 if n mod 4 = 2 then 200
30 goto 300

100 run 2n+1Init
110 run 2n+1
120 goto 400

200 run 4n+2Init
210 run 4n+2
220 goto 400

300 run 4nInit
310 run 4n

400 run PrintSq

500 run check-columms-and-rows
510 run check-diagonals

1000 end ;

: main ( -- )
  21 3
  do i magics loop ;

main

\ ********** the end ***************
 
執行結果：

 
ching@ctt:~$ ./l

AMDX86 ciforth 5.3.0 
fload magic.f
 OK
main

Magic square size : 3 * 3 
The magic sum = 15 
   8   1   6
   3   5   7
   4   9   2

Magic square size : 4 * 4 
The magic sum = 34 
  16   2   3  13
   5  11  10   8
   9   7   6  12
   4  14  15   1

Magic square size : 5 * 5 
The magic sum = 65 
  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

Magic square size : 6 * 6 
The magic sum = 111 
  35   1   6  26  19  24
   3  32   7  21  23  25
  31   9   2  22  27  20
   8  28  33  17  10  15
  30   5  34  12  14  16
   4  36  29  13  18  11

Magic square size : 7 * 7 
The magic sum = 175 
  30  39  48   1  10  19  28
  38  47   7   9  18  27  29
  46   6   8  17  26  35  37
   5  14  16  25  34  36  45
  13  15  24  33  42  44   4
  21  23  32  41  43   3  12
  22  31  40  49   2  11  20

Magic square size : 8 * 8 
The magic sum = 260 
  64  63   3   4   5   6  58  57
  56  55  11  12  13  14  50  49
  17  18  46  45  44  43  23  24
  25  26  38  37  36  35  31  32
  33  34  30  29  28  27  39  40
  41  42  22  21  20  19  47  48
  16  15  51  52  53  54  10   9
   8   7  59  60  61  62   2   1

Magic square size : 9 * 9 
The magic sum = 369 
  47  58  69  80   1  12  23  34  45
  57  68  79   9  11  22  33  44  46
  67  78   8  10  21  32  43  54  56
  77   7  18  20  31  42  53  55  66
   6  17  19  30  41  52  63  65  76
  16  27  29  40  51  62  64  75   5
  26  28  39  50  61  72  74   4  15
  36  38  49  60  71  73   3  14  25
  37  48  59  70  81   2  13  24  35

Magic square size : 10 * 10 
The magic sum = 505 
  92  99   1   8  15  67  74  51  58  40
  98  80   7  14  16  73  55  57  64  41
   4  81  88  20  22  54  56  63  70  47
  85  87  19  21   3  60  62  69  71  28
  86  93  25   2   9  61  68  75  52  34
  17  24  76  83  90  42  49  26  33  65
  23   5  82  89  91  48  30  32  39  66
  79   6  13  95  97  29  31  38  45  72
  10  12  94  96  78  35  37  44  46  53
  11  18 100  77  84  36  43  50  27  59

Magic square size : 11 * 11 
The magic sum = 671 
  68  81  94 107 120   1  14  27  40  53  66
  80  93 106 119  11  13  26  39  52  65  67
  92 105 118  10  12  25  38  51  64  77  79
 104 117   9  22  24  37  50  63  76  78  91
 116   8  21  23  36  49  62  75  88  90 103
   7  20  33  35  48  61  74  87  89 102 115
  19  32  34  47  60  73  86  99 101 114   6
  31  44  46  59  72  85  98 100 113   5  18
  43  45  58  71  84  97 110 112   4  17  30
  55  57  70  83  96 109 111   3  16  29  42
  56  69  82  95 108 121   2  15  28  41  54

Magic square size : 12 * 12 
The magic sum = 870 
 144 143 142   4   5   6   7   8   9 135 134 133
 132 131 130  16  17  18  19  20  21 123 122 121
 120 119 118  28  29  30  31  32  33 111 110 109
  37  38  39 105 104 103 102 101 100  46  47  48
  49  50  51  93  92  91  90  89  88  58  59  60
  61  62  63  81  80  79  78  77  76  70  71  72
  73  74  75  69  68  67  66  65  64  82  83  84
  85  86  87  57  56  55  54  53  52  94  95  96
  97  98  99  45  44  43  42  41  40 106 107 108
  36  35  34 112 113 114 115 116 117  27  26  25
  24  23  22 124 125 126 127 128 129  15  14  13
  12  11  10 136 137 138 139 140 141   3   2   1

Magic square size : 13 * 13 
The magic sum = 1105 
  93 108 123 138 153 168   1  16  31  46  61  76  91
 107 122 137 152 167  13  15  30  45  60  75  90  92
 121 136 151 166  12  14  29  44  59  74  89 104 106
 135 150 165  11  26  28  43  58  73  88 103 105 120
 149 164  10  25  27  42  57  72  87 102 117 119 134
 163   9  24  39  41  56  71  86 101 116 118 133 148
   8  23  38  40  55  70  85 100 115 130 132 147 162
  22  37  52  54  69  84  99 114 129 131 146 161   7
  36  51  53  68  83  98 113 128 143 145 160   6  21
  50  65  67  82  97 112 127 142 144 159   5  20  35
  64  66  81  96 111 126 141 156 158   4  19  34  49
  78  80  95 110 125 140 155 157   3  18  33  48  63
  79  94 109 124 139 154 169   2  17  32  47  62  77

Magic square size : 14 * 14 
The magic sum = 1379 
 177 186 195   1  10  19  28 128 137 146  99 108  68  77
 185 194 154   9  18  27  29 136 145 105 107 116  76  78
 193 153 155  17  26  35  37 144 104 106 115 124  84  86
   5 161 163 172  34  36  45 103 112 114 123 132  85  94
 160 162 171  33  42  44   4 111 113 122 131 140  93  53
 168 170 179  41  43   3  12 119 121 130 139 141  52  61
 169 178 187  49   2  11  20 120 129 138 147 100  60  69
  30  39  48 148 157 166 175  79  88  97  50  59 117 126
  38  47   7 156 165 174 176  87  96  56  58  67 125 127
  46   6   8 164 173 182 184  95  55  57  66  75 133 135
 152  14  16  25 181 183 192  54  63  65  74  83 134 143
  13  15  24 180 189 191 151  62  64  73  82  91 142 102
  21  23  32 188 190 150 159  70  72  81  90  92 101 110
  22  31  40 196 149 158 167  71  80  89  98  51 109 118

Magic square size : 15 * 15 
The magic sum = 1695 
 122 139 156 173 190 207 224   1  18  35  52  69  86 103 120
 138 155 172 189 206 223  15  17  34  51  68  85 102 119 121
 154 171 188 205 222  14  16  33  50  67  84 101 118 135 137
 170 187 204 221  13  30  32  49  66  83 100 117 134 136 153
 186 203 220  12  29  31  48  65  82  99 116 133 150 152 169
 202 219  11  28  45  47  64  81  98 115 132 149 151 168 185
 218  10  27  44  46  63  80  97 114 131 148 165 167 184 201
   9  26  43  60  62  79  96 113 130 147 164 166 183 200 217
  25  42  59  61  78  95 112 129 146 163 180 182 199 216   8
  41  58  75  77  94 111 128 145 162 179 181 198 215   7  24
  57  74  76  93 110 127 144 161 178 195 197 214   6  23  40
  73  90  92 109 126 143 160 177 194 196 213   5  22  39  56
  89  91 108 125 142 159 176 193 210 212   4  21  38  55  72
 105 107 124 141 158 175 192 209 211   3  20  37  54  71  88
 106 123 140 157 174 191 208 225   2  19  36  53  70  87 104

Magic square size : 16 * 16 
The magic sum = 2056 
 256 255 254 253   5   6   7   8   9  10  11  12 244 243 242 241
 240 239 238 237  21  22  23  24  25  26  27  28 228 227 226 225
 224 223 222 221  37  38  39  40  41  42  43  44 212 211 210 209
 208 207 206 205  53  54  55  56  57  58  59  60 196 195 194 193
  65  66  67  68 188 187 186 185 184 183 182 181  77  78  79  80
  81  82  83  84 172 171 170 169 168 167 166 165  93  94  95  96
  97  98  99 100 156 155 154 153 152 151 150 149 109 110 111 112
 113 114 115 116 140 139 138 137 136 135 134 133 125 126 127 128
 129 130 131 132 124 123 122 121 120 119 118 117 141 142 143 144
 145 146 147 148 108 107 106 105 104 103 102 101 157 158 159 160
 161 162 163 164  92  91  90  89  88  87  86  85 173 174 175 176
 177 178 179 180  76  75  74  73  72  71  70  69 189 190 191 192
  64  63  62  61 197 198 199 200 201 202 203 204  52  51  50  49
  48  47  46  45 213 214 215 216 217 218 219 220  36  35  34  33
  32  31  30  29 229 230 231 232 233 234 235 236  20  19  18  17
  16  15  14  13 245 246 247 248 249 250 251 252   4   3   2   1

Magic square size : 17 * 17 
The magic sum = 2465 
 155 174 193 212 231 250 269 288   1  20  39  58  77  96 115 134 153
 173 192 211 230 249 268 287  17  19  38  57  76  95 114 133 152 154
 191 210 229 248 267 286  16  18  37  56  75  94 113 132 151 170 172
 209 228 247 266 285  15  34  36  55  74  93 112 131 150 169 171 190
 227 246 265 284  14  33  35  54  73  92 111 130 149 168 187 189 208
 245 264 283  13  32  51  53  72  91 110 129 148 167 186 188 207 226
 263 282  12  31  50  52  71  90 109 128 147 166 185 204 206 225 244
 281  11  30  49  68  70  89 108 127 146 165 184 203 205 224 243 262
  10  29  48  67  69  88 107 126 145 164 183 202 221 223 242 261 280
  28  47  66  85  87 106 125 144 163 182 201 220 222 241 260 279   9
  46  65  84  86 105 124 143 162 181 200 219 238 240 259 278   8  27
  64  83 102 104 123 142 161 180 199 218 237 239 258 277   7  26  45
  82 101 103 122 141 160 179 198 217 236 255 257 276   6  25  44  63
 100 119 121 140 159 178 197 216 235 254 256 275   5  24  43  62  81
 118 120 139 158 177 196 215 234 253 272 274   4  23  42  61  80  99
 136 138 157 176 195 214 233 252 271 273   3  22  41  60  79  98 117
 137 156 175 194 213 232 251 270 289   2  21  40  59  78  97 116 135

Magic square size : 18 * 18 
The magic sum = 2925 
 290 301 312 323   1  12  23  34  45 209 220 231 242 163 174 104 115 126
 300 311 322 252  11  22  33  44  46 219 230 241 171 173 184 114 125 127
 310 321 251 253  21  32  43  54  56 229 240 170 172 183 194 124 135 137
 320 250 261 263  31  42  53  55  66 239 169 180 182 193 204 134 136 147
   6 260 262 273 284  52  63  65  76 168 179 181 192 203 214 144 146 157
 259 270 272 283  51  62  64  75   5 178 189 191 202 213 224 145 156  86
 269 271 282 293  61  72  74   4  15 188 190 201 212 223 234 155  85  96
 279 281 292 303  71  73   3  14  25 198 200 211 222 233 235  84  95 106
 280 291 302 313  81   2  13  24  35 199 210 221 232 243 164  94 105 116
  47  58  69  80 244 255 266 277 288 128 139 150 161  82  93 185 196 207
  57  68  79   9 254 265 276 287 289 138 149 160  90  92 103 195 206 208
  67  78   8  10 264 275 286 297 299 148 159  89  91 102 113 205 216 218
  77   7  18  20 274 285 296 298 309 158  88  99 101 112 123 215 217 228
 249  17  19  30  41 295 306 308 319  87  98 100 111 122 133 225 227 238
  16  27  29  40 294 305 307 318 248  97 108 110 121 132 143 226 237 167
  26  28  39  50 304 315 317 247 258 107 109 120 131 142 153 236 166 177
  36  38  49  60 314 316 246 257 268 117 119 130 141 152 154 165 176 187
  37  48  59  70 324 245 256 267 278 118 129 140 151 162  83 175 186 197

Magic square size : 19 * 19 
The magic sum = 3439 
 192 213 234 255 276 297 318 339 360   1  22  43  64  85 106 127 148 169 190
 212 233 254 275 296 317 338 359  19  21  42  63  84 105 126 147 168 189 191
 232 253 274 295 316 337 358  18  20  41  62  83 104 125 146 167 188 209 211
 252 273 294 315 336 357  17  38  40  61  82 103 124 145 166 187 208 210 231
 272 293 314 335 356  16  37  39  60  81 102 123 144 165 186 207 228 230 251
 292 313 334 355  15  36  57  59  80 101 122 143 164 185 206 227 229 250 271
 312 333 354  14  35  56  58  79 100 121 142 163 184 205 226 247 249 270 291
 332 353  13  34  55  76  78  99 120 141 162 183 204 225 246 248 269 290 311
 352  12  33  54  75  77  98 119 140 161 182 203 224 245 266 268 289 310 331
  11  32  53  74  95  97 118 139 160 181 202 223 244 265 267 288 309 330 351
  31  52  73  94  96 117 138 159 180 201 222 243 264 285 287 308 329 350  10
  51  72  93 114 116 137 158 179 200 221 242 263 284 286 307 328 349   9  30
  71  92 113 115 136 157 178 199 220 241 262 283 304 306 327 348   8  29  50
  91 112 133 135 156 177 198 219 240 261 282 303 305 326 347   7  28  49  70
 111 132 134 155 176 197 218 239 260 281 302 323 325 346   6  27  48  69  90
 131 152 154 175 196 217 238 259 280 301 322 324 345   5  26  47  68  89 110
 151 153 174 195 216 237 258 279 300 321 342 344   4  25  46  67  88 109 130
 171 173 194 215 236 257 278 299 320 341 343   3  24  45  66  87 108 129 150
 172 193 214 235 256 277 298 319 340 361   2  23  44  65  86 107 128 149 170

Magic square size : 20 * 20 
The magic sum = 4010 
 400 399 398 397 396   6   7   8   9  10  11  12  13  14  15 385 384 383 382 381
 380 379 378 377 376  26  27  28  29  30  31  32  33  34  35 365 364 363 362 361
 360 359 358 357 356  46  47  48  49  50  51  52  53  54  55 345 344 343 342 341
 340 339 338 337 336  66  67  68  69  70  71  72  73  74  75 325 324 323 322 321
 320 319 318 317 316  86  87  88  89  90  91  92  93  94  95 305 304 303 302 301
 101 102 103 104 105 295 294 293 292 291 290 289 288 287 286 116 117 118 119 120
 121 122 123 124 125 275 274 273 272 271 270 269 268 267 266 136 137 138 139 140
 141 142 143 144 145 255 254 253 252 251 250 249 248 247 246 156 157 158 159 160
 161 162 163 164 165 235 234 233 232 231 230 229 228 227 226 176 177 178 179 180
 181 182 183 184 185 215 214 213 212 211 210 209 208 207 206 196 197 198 199 200
 201 202 203 204 205 195 194 193 192 191 190 189 188 187 186 216 217 218 219 220
 221 222 223 224 225 175 174 173 172 171 170 169 168 167 166 236 237 238 239 240
 241 242 243 244 245 155 154 153 152 151 150 149 148 147 146 256 257 258 259 260
 261 262 263 264 265 135 134 133 132 131 130 129 128 127 126 276 277 278 279 280
 281 282 283 284 285 115 114 113 112 111 110 109 108 107 106 296 297 298 299 300
 100  99  98  97  96 306 307 308 309 310 311 312 313 314 315  85  84  83  82  81
  80  79  78  77  76 326 327 328 329 330 331 332 333 334 335  65  64  63  62  61
  60  59  58  57  56 346 347 348 349 350 351 352 353 354 355  45  44  43  42  41
  40  39  38  37  36 366 367 368 369 370 371 372 373 374 375  25  24  23  22  21
  20  19  18  17  16 386 387 388 389 390 391 392 393 394 395   5   4   3   2   1
 OK

附註 ： 20241111 重新整理後貼出。