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Note: Run times are for a 2.2 GHz PC.
Makes the 880 order 4 magic squares. Output is a .txt file.
Makes the 275,305,224 order 5 magic squares.
Files are output in folder C:\Order5[_n]. There are 25 .txt files, one each for the squares with the same center value. The files contain only the squares in a single column. Numbers are separated by white space characters, (blank, newline).
Run time is 29 minutes.
WARNING: The files are large, ranging from 341 MB to 1,492 MB, (total 21 GB).
Makes the 174,240 concentric order 5 magic squares. Output is a .txt file. The last 2880 squares in the file are consecutively concentric.
Makes the 2880 consecutively concentric order 5 magic squares. Output is a .txt file.
Makes special order 5 magic squares. The types made are associative, pandiagonal, concentric, and ultramagic. Files are output in folder C:\Order5Special[_n]. Run time is 9 minutes.
Computes the number of order 5 magic squares. Run time is 21 minutes.
Order 6 concentric magic squares, (736,347,893,760).
Makes 4x4 center squares and border groups. For an input range of partitions, the output is:
Files are output in folder C:\Order6C[_n].
Makes a sample of the squares. One square is output for each of the center/border partitions, (22,145 squares). Output is a .txt file. Run time is 5 minutes 37 seconds.
Computes the number of order 6 concentric magic squares. Run time is 9 minutes.
Order 7 concentric magic squares, (3,835,791,613,181,952,000).
Computes the number of order 7 concentric magic squares. Run time is 8 hours 30 minutes.
Makes consecutively concentric magic squares and bones. Makes one distinct square of each order using an algorithm developed for the HP41C pocket calculator. Files are output in folder C:\BorderedSquare[_n].
Makes consecutively concentric magic squares and bones. Makes many distinct squares by independently turning each nested border and the center through a randomly selected rotation or reflection. Files are output in folder C:\BorderedSquares[_n].
Input for these programs is a .txt file containing one or more number squares of the same order. The text file must contain only the square numbers separated by white space characters, (blank, horizontal tab, newline).
You will be prompted first to input the order of the squares, and, then the file name. The file name may be the absolute path name or the path name relative to the folder containing the program. It is not necessary to enter the .txt extension. For example, if program Frenicle is in folder C:\Squares and the file is C:\Squares\order4squares.txt, the file name may be entered as any of:
Puts squares in Frénicle standard form and sorts them in ascending order. The output file is <in file name>Frenicle[_n].txt
Checks if squares are magic.
The program classifies each square as normal magic, other magic, or not magic. If the squares are not all of the same class, they are written to separate files: NormalMagic, OtherMagic, NotMagic. The files are written to folder Order<N>Squares[_n].
Computes and displays the water retention patterns of number squares. Water retention is an idea of Craig Knecht. The program is based on an algorithm of Gareth McCaughan.
See requirements for the input file under the Utility Programs heading. An example text file of the 880 order 4 magic squares is provided.
The output file is <in file name>Water[_n].html. The waterStyle.css file must be put in the folder with the html file for your browser to display the result correctly. Here is an example:
CAUTION: Avoid creating overly big html files. A guideline for the limit on the number of squares in a text file is: 2000 for order 5, 500 for order 10, or 5 for order 100.