| Magic Series |
| Table of Contents |
| Introduction (Easy !) | |
| What are magic series and what can we do with them? | |
| How to count magic series (Interesting !) | |
|
How can we calculate the number of magic series for a certain order? | |
| Theory of magic series (pdf) (Mathematical !) | |
|
A mathematical definition and an iterative algorithm for counting magic series. Note that I wrote this in September 2002 without knowing that Henry Bottomley (Great Britain) made a similar approach some months before. Have a look at his excellent partition calculator (external link). Robert Gerbicz (Hungary) presented a new algorithm in April 2006. It is faster and needs less memory. Visit his homepage and read about his C-program (external link). | |
| Number of Series up to order 100 (Old but useful !) | |
| These numbers have an accuracy of 15 digits. (2005-02-02) | |
| Exact number of magic series (Impressive !) | |
|
The number of magic order-50 series has got more than 100 digits. Breakthrough in 2006: Robert Gerbicz (Hungary) extended the table dramatically up to order 150. | |
| Magic series of cubes and hypercubes (Magic3 !) (Update 2007) | |
|
There are also series for magic objects of higher dimensions. | |
| Formulae for random dimensions (Brandnew !) (New 2007) | |
|
Impressive new strategies to enumerate magic series in various dimensions. | |
| Multimagic series (Important !) | |
|
These series can be used to construct multimagic squares and cubes. Read more on Christian Boyer's famous site www.multimagie.com (external link). | |
| Link to other pages: | Number of magic squares of higher orders |
|
Read how magic series can be used to estimate the number of magic squares. | |