|
Enumeration Magic Squares of Subtraction (5 x 5)
Associated
The enumeration of order 5 Associated Magic Squares of Subtraction (Res5 = 13) has been executed with
routine SubtrSqrs5b and is summarised below:
| a(25) |
n51 |
sec |
| 1 |
513824 |
418 |
| 2 |
376192 |
436 |
| 3 |
272896 |
221 |
| 4 |
183744 |
154 |
| 5 |
103008 |
126 |
| 6 |
67360 |
81 |
| 7 |
31552 |
32,5 |
| 8 |
14496 |
12,3 |
| 9 |
1152 |
2,5 |
| Total |
1564224 |
1483,3 |
|
|
Subject routine counted 1.564.224 Essential Different Associated Magic Squares of Subtraction in 1483 seconds,
which corresponds with 6.256.896 (4 * 1.564.224) Unique Associated Magic Squares of Subtraction.
|
Attachment 5.1
|
shows for a(25) = 1, 2 ... 9 the first occurring Associated Magic Square of Subtraction.
|
|
Attachment 5.5
|
shows miscellaneous Associated Magic Squares of Subtraction with Square - or (and) Diamond Inlays,
s3 = 39.
|
|
Attachment 5.4
|
shows the two Associated Magic Squares of Subtraction for which the Main - and Broken Diagonals
sum to s5 = 65.
|
Crosswise Symmetric
The enumeration of order 5 Crosswise Symmetric Magic Squares of Subtraction (Res5 = 13) has been executed with
routine SubtrSqrs5c and is summarised below:
| a(25) |
n52 |
sec |
| 1 |
1027648 |
10024 |
| 2 |
824080 |
9263 |
| 3 |
801748 |
8560 |
| 4 |
645098 |
7257 |
| 5 |
587238 |
6382 |
| 6 |
480843 |
5113 |
| 7 |
444440 |
4784 |
| 8 |
346114 |
3898 |
| 9 |
304327 |
3323 |
| 10 |
242805 |
2415 |
| 11 |
179420 |
2015 |
| 12 |
111823 |
1547 |
| 14 |
104377 |
1518 |
| 15 |
60468 |
1047 |
| 16 |
32675 |
633 |
| 17 |
27877 |
498 |
| 18 |
15890 |
319 |
| 19 |
10108 |
203 |
| 20 |
5449 |
117 |
| 21 |
3542 |
58,5 |
| 22 |
926 |
23,5 |
| Tota4 |
6256896 |
68998 |
|
|
|
Subject routine counted 6.256.896 Unique Crosswise Symmetric Magic Squares of Subtraction in 19,2 hours.
Attachment 5.3 shows
for a(25) = 1 ... 12, 14 ... 22 the first occurring Crosswise Symmetric Magic Square of Subtraction.
Simple Magic
The enumeration of order 5 Simple Magic Squares of Subtraction is beyond the scope of this Exhibit 5.
Attachment 5.2 shows
a few Simple Magic Squares of Subtraction with different residuum values.
|
