Downloads

The software on this site may be used freely.
You should use only if you agree to the freeware disclaimer.

To make a copy of a console:
  Click the upper left corner button, and Edit, Select All.
  Click the upper left corner button, and Edit, Copy.
  Paste to a text file.

To paste input, such as, a file name, into a console:
Copy the file name from somewhere.
Click the upper left corner button, and Edit, Paste.

There are source code files and CLR and Win32 applications for the programs described below.

Adjacent

Associative

Bordered

BorderedSquare	Win32 exe	CLR exe	C code

Makes bordered magic squares. Makes one distinct square of each order using an algorithm developed for the HP-41C pocket calculator. Output files are in folder BorderedSquare[_n].

BorderedSquares	Win32 exe	CLR exe	C code

Makes bordered magic squares. Makes many distinct squares by randomly:

arranging row and column value pairs, (except corners)
rotating each border and the center
selecting one of the 880 4x4s as center for even order squares

Output files are in folder BorderedSquares[_n].

BorderedSquares1	Win32 exe	CLR exe	C code

An earlier version that made many fewer distinct squares, only randomly rotating each nested border and the center. Output files are in folder BorderedSquares[_n].

Bordering

Composite

Franklin

Most-perfect

Pandiagonal

Self-complement

SelfComplementSquares	Win32 exe	CLR exe	C code

Makes side-to-side symmetric self-complement even order magic squares. Output files are in folder SelfComplementSquares[_n].
To make associative self-complement magic squares, use program AssociativeSquares

Symlateral

Order 4

Order 5

Order5	Win32 exe	CLR exe	C code

Makes the 275,305,224 order 5 magic squares.

Files are output in folder 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).

WARNING: The files are large, ranging from 341 MB to 1,492 MB, (total 21 GB).

Order5Special	Win32 exe	CLR exe	C code

Makes special order 5 magic squares. The types made are associative, concentric, bordered, inlaid corner, inlaid side, pandiagonal, ultramagic. Files are output in folder Order5Special[_n].

Order 6 Concentric

Order5Count	Win32: 7 minutes	CLR: 11 minutes	C code

Order6C	Win32 exe	CLR exe	C code

Makes 4x4 center squares and border groups. For an input range of partitions, the output is:

for each partition that has a 4x4 center square:
- a file of the border groups
- a file of the 4x4 center squares
a summary file

See Order6CDoc.txt and Order6CExamples.txt. Output files are in folder Order6C[_n].

Order 7 Concentric

Order6Ccount	Win32: 5 minutes	CLR: 7 minutes	C code

Order7Ccount	Win32: 4 h 40 m	CLR: 5 h 23 m	C code

Computes the number of order 7 concentric magic squares, (3,835,791,613,181,952,000). See Order7CDoc.txt. Only the source code is provided.

Utility Programs

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 can 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 can be entered as any of:

Bones	Win32 exe	CLR exe	C code

Changes squares to or from bones format. Square numbers must be in the range 1 to N² or 0 to N²-1 for sensible results. Output .html file(s) are in folder ToFromBones<N>[_n]. If the input file is large, output may be split into a number of files.

CopySquaresByNumber	Win32 exe	CLR exe	C code

Copies squares from a file. Squares to copy are chosen by a number or number range. The output file is Order<N>Copy<num>[_n].txt or Order<N>Copy<num1>to<num2>[_n].txt

Frenicle	Win32 exe	CLR exe	C code

Puts squares in Frénicle standard form and sorts them in ascending order. The number of duplicate squares is reported and duplicates are not output. The output file is <in file name>Frenicle[_n].txt

GetMagic	Win32 exe	CLR exe	C code

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].

GetType	Win32 exe	CLR exe	C code

Checks the type of each square as: not magic, normal semi-magic, other semi-magic, normal magic, other magic. If the type is normal magic, checks other properties: adjacent corner, adjacent side, associative, concentric, bordered, bordering, symlateral, pandiagonal, compact, complete, bent diagonal, Franklin, zigzag, self-complement. See notes. Results are written to <in file name>TypeSummary[_n].txt.

Rotate	Win32 exe	CLR exe	C code

Rotates squares to a different aspect chosen by the rotation number:


     Number                   Rotation
    --------    -----------------------------------------------------
        0                       none
        1                   clockwise 90°
        2                       180°
        3                counterclockwise 90°

        4       180° about middle vertical or Y axis,   (= mirror)
        5       180° about main forward diagonal,       (= mirror + 1)  
        6       180° about middle horizontal or X axis, (= mirror + 2)  
        7       180° about main back diagonal,          (= mirror + 3)

        8                       all

Transform

Transforms1_2	Win32 exe	CLR exe	C code

Transforms squares using transform 1 and/or transform 2. For each squares file, you can do a transform and then opt to do another transform of that transform. If declined, you can opt to do another transform on the original squares. If declined, you can opt to transform another file of squares. The transform is selected by the number of rows entered, (1 or 2).

The flow chart is:


          --------------->--------- enter the order
         ^                                 |
         |                        enter the file name
         |                                 |
         |    ----------->--------- enter the rows(s)
         |   ^   ^                         |
         |   |   |                   transform squares
         |   |   |                         |
         |   |    <- YES <- transform transformed squares?
         ^   ^                             |
         |   |                             NO
         |   |                             |
         |    <----- YES <--- transform original squares?
         |                                 |
         |                                 NO
         |                                 |
          <--------- YES <----- transform another file?
                                           |
                                           NO
                                           |
                                          end

Transforms1_2All	Win32 exe	CLR exe	C code

For each square in an input file, makes (a sample of) all possible squares from repeated transform 1 and/or transform 2. Output files are in folder Order<N>XForm[_n]. There is one file for each square in the input file. The first square in each output file is the original square.

Complement	Win32 exe	CLR exe	C code

Makes the complementary squares. The output file is <in file name>Complement[_n].txt.
Self-complement squares are also written to <in file name>SelfComplement[_n].txt

AssocPan	Win32 exe	CLR exe	C code

For doubly even orders, transforms associative magic squares to or from pandiagonal complete magic squares. Output file(s) are in folder Order<N>AssocPan[_n]. If the input file is large, output may be split into a number of files.

Most-perfectToFranklin	Win32 exe	CLR exe	C code

For orders that are a multiple of 8, transforms most-perfect squares to Franklin magic squares. Output file(s) are in folder Order<N>Franklin[_n]. If the input file is large, output may be split into a number of files.

Water Retention

WaterRetention	Win32 exe	CLR exe	C code

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. Output .html files are in folder Water<N>[_n]. If the input file is large, output may be split into a number of files. Here is an output example:

WaterRetention3D	Win32 exe	CLR exe	C code

Displays a 3-dimensional view of water retention. The code for the 3D view was written by Claudio Rocchini during the Zimmermann contest. Land is shown in shades of green, water in blue, and the start of spillways between water bodies or out of the square in yellow. For water, the bottom elevations are shown. Here are examples:

Output files are in folder Water<N>_3D[_n]. The files are in Scalable Vector Graphics (SVG) format. There is one .svg file for each square in the input file.

You may need to install a viewer like Win 98-XP from Adobe, before your browser will open .svg files. Another way is to download and run a program such as Windows - installer from Inkscape. With Inkscape you can open a .svg file and save it as a .png.

WaterRetentionSort	Win32 exe	CLR exe	C code

Sorts squares in decreasing order of water retention. The number of duplicate squares is reported and duplicates are not output. The output file is <in file name>WRsort[_n].txt. A summary file is also written.

formatZtoW	Win32 exe	CLR exe	C code

Re-formats squares in Zimmermann contest format to the white space separated format used by programs on this site. Squares are output in folder WfromZ[_n].