3-19-2009

 

File produced from F1 compiler and example code at F1 website for generating all order 5 magic squares

 

 

 

275,305,224 order 5 magic squares water retention

 

Col 1 = total units water retained

Col 2 = number of squares retaining that amount of water

 

 

 

Col 1 col 2

 

 

0 3254785

1 3288269

2 3974487

3 5244340

4 5975214

5 7121279

6 8031236

7 8910016

8 9647721

9 10361130

10 10823964

11 11177044

12 11447297

13 11391597

14 11414725

15 11221534

16 11006925

17 10619637

18 10364695

19 9800501

20 9476800

21 8858022

22 8432152

23 7779143

24 7318183

25 6640187

26 6201120

27 5559520

28 5099167

29 4504819

30 4129250

31 3596688

32 3238216

33 2807344

34 2489417

35 2143527

36 1862240

37 1595758

38 1380461

39 1169737

40 1018778

41 838174

42 725801

43 593718

44 507906

45 421031

46 346302

47 289755

48 242537

49 191180

50 161815

51 128203

52 105443

53 80068

54 69808

55 53472

56 45376

57 36958

58 27877

59 18434

60 14710

61 9187

62 6706

63 5132

64 3458

65 2472

66 1699

67 772

68 269

69 36

70

 

 

 

 

         3254785 order 5 magic squares retain no water

         36 order 5 magic squares retain 69 units of water

 

Hiccup of smooth progression for 13 units retained

 

 

 

Table 2

 

Col 1 = number of interior cells retaining

Water

 

Col 2 = number of order 5 magic squares

 

Col 1 Col 2

 

 

 

0 3254785

1 26507990

2 73823483

3 93220761

4 57984351

5 17803844

6 2565940

7 144070

8

9

 

 

 

 

         there are no order 5 magic squares that have 8 or 9 interior cells retaining water

 

 

 

 

 

 

 

 

#1. 361 hours for the F1 to produce all 275305224 order 5 magic squares

#2. 39 gigabytes to store the .log file as it comes from the F1 compiler

#3. 4 hours for my retention program to sort through the 39 gig file and produce the above results

 

 

 

 

 

 

Topographical Model

 

36 examples order 5 magic square retain 69 units of water

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure below is this pattern the least prevalent retention pattern?

 

 

1)    144,070 of 275,305,224 order 5 magic squares have 7 interior cells retaining.

2)    Only three different patterns for 7 cells retaining with occurrence shown above

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure above shows occurrence of various patterns for complete set order 5 magic squares