This page contains links to files related to number patterns that may be downloaded.
Downloading a desired file is as simple as just clicking on the link.
These posted files as ready to use if they are not too large. The larger files will be supplied in compressed form to save storage space and download time

Included are MS Word, TXT,  and Adobe PDF documents and Excel spreadsheets.
None of these files include scripts.

Also, included are listings for a number of Basic programs. Most are small and of limited use, but I include them to give modern readers a taste for the early days of personal computing.

March 2013  Uploaded most of J. R. Hendricks out-of-print books for downloading as eBooks.

About viruses
I meticulously protect my computer from viruses by scanning all drives periodically, scanning all incoming email, MS Word, Excel, and program files.

However, while I believe all the files posted here are free of viruses, it is expedient on the downloader to rescan these files.

I expect no problems as a result of downloading any of the files posted here, but accept no responsibility for damage of any kind caused by such downloading .


Documents               Spreadsheets                         Programs                  J. Hendricks Books


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MS Word and .pdf documents


402 kb

144 order-5 pandiagonal magic squares derived from the 36 essentially different ones.

175 kb

All 880 4x4 magic squares sorted by groups. (unzipped 661 kb)

175 kb

All 880 4x4 magic squares sorted by Frenicle index. (unzipped 667 kb)


33 kb

A number pattern based on the cyclic number 1/17. I did this about 1960.


236 kb

Notes and lists of PPDI numbers and RDI cycles.


29 kb

A small text file of star A solutions, orders 15 - 50,  supplied by Simon Whitechapal, Sept. 9, 2003.

ArnouxCube.doc 64 kb

Some text description and a listing of the 17 horizontal planes of G. Arnoux's 1887 perfect cube.

Barnard-11.doc 44 kb

Listings of F. A. P. Barnard's two order 11 Perfect magic cubes of 1888

CubeComparison.doc 716 kb

A table comparing 16 characteristics of my collection of approximately 340 magic cubes.

Karnaugh-to-Cubes.doc 133 kb

A paper by S. Meine and D. Schuett which transforms Karnaugh maps into magic squares or cubes.

Tess_58.doc 100 kb A 6 page MS Word document with complete listings for all 58 of the order-3 magic tesseracts.
Tess_58.pdf 140 kb Identical to above, only in Adobe pdf format.
Kumar_12-KT,doc 43 kb Listing for Awani Kumar's order-12 Magic cube Knight tour of June 2007
New_Advances_(4).doc 54 kb A condensed report by Lee Sallows of which the following 2 articles resulted.
880 New Squares.doc 127 kb Lee Sallows shows a set of 880 order-4 magic squares using the number set 1 to 18 with no 5 or 14.
MS1040.txt 75 kb Lee Sallows shows a set of 1040 order 4 magic squares using the number set -8 to -1 and 1 to 8. He conjectures that this is the only set possible that contains more then 880 magic squares.
Non-normal Graphic Types 145 kb Lee Sallows identifies  22 additional  Dudeney style diagrams and shows a representative magic square for each.
Bao Qi-shou.pdf 1569 kb Lih, Ko-Wei, Bao Qi-shou and his Polyhedral Hun Yaun Yu. 1993, Cheng-hung Lin and Daiwie Fu (Eds.), Philosophy and Conceptual History of Science in Taiwan, pps 209-220. 12 page English paper on Bao Qi-shou. Referenced in Perimeter-4.htm.
Graph Labelling.pdf 1951 kb Lih, Ko-Wei, On Magic and Consecutive Labelling of plane graphs, 1980, 33 pages, , Utilitas Mathematica, 24(1983), p.165-p.197. No mention of Bao, but lots of magic labelled graphs.

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MS Excel


49 kb

A template I use for testing if a square is magic. Presently tests orders 3-9 and 16.


37 kb

Tests order-13 magic squares for Quadrant Magic Square properties.

177 kb

Test spreadsheet for the variation of Franklin's newly discovered 16x16, as shown on my Franklin page.

Prime Heterosquares

59 kb

An Excel spreadsheet listing many Anurag Sahay's heterosquare and anti-magic squares.


738 kb Am Excel document sorted list of all 3600 5x5 pandiagonal magic squares.

123 kb

A zipped Excel document sorted list of all 3600 5x5 pandiagonals. 144 kb

A zipped Excel document comparing features of 7 order 8 Franklin type compact squares,

Hypercube Generator-3.xls 104 kb

Generate the 4 basic cubes and 58 basic tesseracts of order 3 from signature catalogs. 199 kb

An archive of 6 spreadsheets I used to check out these patterns. 1218 kb

An archive of Nakamura's order 16 diagonal nested magic cube with test spreadsheets of the other 6 even orders <16. 262 kb

Cubes of orders 3 to 6 as shown on the Perfect Cubes-2 page but in test spreadsheets. 382 kb

Cubes of orders 7 to 9 as shown on the Perfect Cubes-2 page but in test spreadsheets. 224 kb

Cubes of orders 10 and 11 as shown on the Perfect Cubes-2 page but in test spreadsheets.

QMS_4-12-Patterns.xlsx 82 kb The quadrant patterns for orders 4, 8 and 12. and some squares and tests
QMS_16-Patterns.xlsx 172 kb The quadrant patterns for order 16 and  and some squares and tests
Tesseract Surface-KT.xls 48 kb A diagram of the flattened order-8 tesseract with a magic knight tour

MS Excel files by John Hendricks


33 kb 3-D diagrams of 2 order 3 cubes are displayed with provision to enter values for c, x, y and z. A catalog of the values for each of the four basic magic cubes is given. 1 of the two diagrams can be set up to display a basic cube, then values from another corner of this cube may be entered to display one of it's 48 aspects in the second diagram.


16 kb This interactive display reveals the number of each of 13 characteristics for the order and dimensions of the object entered.


303 kb This program uses Digital Equations to trace a path through a magic square.


43 kb Investigate the world's first perfect magic Tesseract. This interactive spreadsheet displays the 16 numbers in any of the 40 lines starting at any coordinate of this order 16, dimension 4 hypercube.
Perfect means that this tesseract has all pan-quadragonals correct, and all 64 cubes and 1536 squares contained in it are also perfect.


38 kb 3-D diagrams of each of the 4 order 3 basic magic cubes are shown in this interactive spreadsheet. Provision is made for entering values for the lower left corner and the 3 numbers adjacent to it, so as to provide a different aspect of  one of these 4 cubes.

2-D Aspects.xls

17 kb Shows any of the 8 variations of the order-3 magic square.

3-D Aspects.xls

36 kb Shows any of the 38 variations of the 4 order-3 magic cubes.

4-D Aspects.xls

151 kb Shows any of the 384 variations of the 58 order-3 magic tesseracts.

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I have a great many programs on recreational mathematics that have been written in QuickBasic 4.5 (or older Basics) over about 35 years.
Most of them are now of no practical value (and Quick Basic is now an antiquated language). However, modern readers may like to read the listings to get a taste of early amateur programming.

These programs could have been posted as executable files, but then could not be freely downloaded because of Internet security. Therefore, the source code is posted here as a text file.

 That leaves you, the reader, with three options.

  1. If you have QB45 installed on your computer, you may load this file directly into QB.

  2. You may rewrite the source code for Visual Basic, or simply look at the text file to get ideas.
    ( Because some of  this code is 1/3 century old, and also because I am not a trained programmer, do not expect to see clever programming examples.)

  3. E-mail me for a copy of the program.

Bytmaker.txt 2kb Steps through the decimal #'s 1-255 showing the binary bits and ASCII characters.
Conv2Dec 3kb A simple but useful program that converts 2 to 4 digit base 2 to 9 numbers to decimal.
DecRnum.txt 5kb Counting 1 to 2000 and conversion between Decimal and Roman Numerals.
Factors.txt 2kb Finds factor pairs and determines if # is square, prime, perfect, abundant, or deficient.
FastPie.txt 1 kb A fast method of computing Pi to 15 decimal places.
FourSqr.txt 4kb Finds all 880 order-4 magic squares and lists them in Frenicle index order.
HCFactor.txt 2kb Finds the highest common factor of 2 integers with a total of <26 digits.
Magic12.txt 59 kb Source code for a program first written in 1993 to demonstrate various m.square routines.
MgSqrOdd.txt 3kb Constructs odd order m. squares. choice of size 3-13, starting number and start position.
Pan5x5.txt 17 kb Source for a program that produces a list of 144 or all 3600 order-5 pan magic squares.
PerProd.txt 2kb A Perfect Product number is one whose prime factors are all unique prime numbers.
PFactors.txt 2kb Finds the prime factors of a number of up to 7 digits.
PrimeNum.txt 9kb Generate prime numbers to 32767. Also test for. Also 3 different prime plots.
Sqr4Comp.txt 8kb Finds complement pairs and other features from data generated by FourSqr.bas.
Star_6.txt 12kb One of the series of programs I used to find magic star solutions. This one finds order-6.

John Hendricks Books

All of John Hendricks self-published books have been converted to PDF eBooks.  I have made the smaller books available for free downloading
from this page. At a later date I may add the larger books, so please advise me by email if you download any of these.
Click on the link to start the download. Then view with Adobe Reader.

4-D Images.pdf 8,328 kb Images From the Forth Dimension, self-published, 1993, 26 pages plus covers, 8.5" x 11" flat stitched.
Hendricks lattice representation of the tesseract showing the 8 cubes. also covers Pentatope, Tetratope & hypersphere.
Bi-MagicC-25.pdf 1,541 kb A Bimagic Cube of Order 25, self-published, 2000, 0-9684700-7-6, 18 pages plus covers, 8.5" x 11" flat stitched. Includes theory, equations, and a computer program to output the cube.
Bi-MagicC-25-2.pdf 18,178 kb A Bimagic Cube of Order 25 v. 2, self-published, 2000, 0-9684700-7-6, 48 pages plus covers, 8.5" x 11" flat stitched. This beautifully printed, self-published booklet edited by Holger Danielsson lists the complete cube in diagram and text form.
BimagicS-9.pdf 1,468 kb

Bimagic Squares: Order 9, self-published, 1999, 16 pages plus covers, 8.5" x 11" flat stitched.
Sent to J. Hendricks by David M. Collison (1937-1991 with no explanation just before he died.

Inlaid comples-24.pdf 4,719 kb An Inlaid Complex Magic Square of Order-19 With Interchangable Parts, 20 pages plus covers, 8.5" x 11" flat stitched. Included in pp 82-99 of  Inlaid Magic Squares  and Cubes. 2nd Edition.
Inlaid Order-10.pdf 4,089 kb

A Magic cube of Order-10, Unpublished, 1998, 23 pages 8.5 " x 11" flat stitched.
With an inlaid cube of order-6 and adorned with 12 inlaid magic squares of order-6.

InlaidTess.pdf 2,066 kb

An Inlaid Magic Tesseract, A poster folded to 8 pages 8.5" x 11",  Published for free distribution with sale of other books. An order-6 tesseract with an inlaid order-3 tesseract..

Lexicon-v2.pdf 2,072 Kb Magic Square Lexicon: Illustrated. HDH Publishing, 2000, 0-9687985-0-0.Co-authored with Harvey D. Heinz
239 terms defined, about 200 illustrations and tables, 171 captioned.
Magic Hypercubes.pdf 7,449 Kb Magic Hypercubes, self-published, 1988, 22 pages plus covers, 8.5" x 11" flat stitched.
Theory and examples of all 59 order-3 Tesseracts.
MS-of-DO-2.pdf 2,962 Kb Magic Squares of Doubled Order, 2nd Edition, 16 pages 8.5 " x 11" flat stitched. Edited by Holger Danielsson
This typeset edition includes an alternative method of construction these magic squares. Includes examples of order-10 and 18 inlaid magic squares.
Order3-MT.pdf 2,786 Kb All Third-Order Magic Tesseracts, Self-published, 1999, 0-9684700-2-5, 36 pages plus covers, 8.5" x 11" flat stitched, 60+ diagrams.
Some theory including discussion of species. Diagrams of all 58 Order-3 magic tesseracts.
Perfect.pdf 3,464 Kb Perfect n-Dimensional Magic Hypercubes of Order 2n, Self-published, 1999, 0-9684700-4-1. 36 pages plus covers, 8.5" x 11" flat stitched, some diagrams.
Theory with examples for a cube, tesseract, 5-D and 6-D hypercubes.
A Basic program to generate any desired path for a 5-D order-32 nasik magic hypercube!
Z-Hendricks_Permission.pdf 378 Kb Copy of agreement to allow free distribution of John Hendricks material.


This page was originally posted September 2001
It was last updated March 13, 2013
Harvey Heinz
Copyright 1998-2009 by Harvey D. Heinz