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