talkmagic.co.uk

Lawrence wrote:The mathematician in me wants to point out that your picture technically isn't a hexagon.

The magician in me wants to say it's probably in Fulves; it'll be in Fulves, yeah? It usually is

A magic hexagon of order n is an arrangement of numbers in a centered hexagonal pattern with n cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant. A normal magic hexagon contains the consecutive integers from 1 to 3n2 − 3n + 1. It turns out that magic hexagons exist only for n = 1 (which is trivial) and n = 3. Moreover, the solution of order 3 is essentially unique.[1] Meng also gave a less intricate constructive proof.[2]

The order-3 magic hexagon has been published many times as a 'new' discovery. An early reference, and possibly the first discoverer, is Ernst von Haselberg (1887).

Although there are no normal magical hexagons with order greater than 3, certain abnormal ones do exist. In this case, abnormal means starting the sequence of numbers other than with 1.

ACE T wrote:I think Lawrence was saying that Karl Fulves may have written up this routine in one of his many publications.

I can't help you out as to which one though. Here's a list...

http://en.wikipedia.org/wiki/Karl_Fulves" target="_blank

Mandrake wrote:According to Wikki which shows the same hexagon as above:

A magic hexagon of order n is an arrangement of numbers in a centered hexagonal pattern with n cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant. A normal magic hexagon contains the consecutive integers from 1 to 3n2 − 3n + 1. It turns out that magic hexagons exist only for n = 1 (which is trivial) and n = 3. Moreover, the solution of order 3 is essentially unique.[1] Meng also gave a less intricate constructive proof.[2]

The order-3 magic hexagon has been published many times as a 'new' discovery. An early reference, and possibly the first discoverer, is Ernst von Haselberg (1887).

Although there are no normal magical hexagons with order greater than 3, certain abnormal ones do exist. In this case, abnormal means starting the sequence of numbers other than with 1.

In other words, as M ("Sit down 007") is known it's fairly easy to work out the sequence of numbers on the rows, a bit like a variation on the magic square - a square with the corners knocked off if you like!

JustMe wrote:Thanks that actually might help me!!! Though what I want is a bit different. The pattern in this wiki hexagon depends on the numbers in the cells but what I want to achieve is to make it depend on the moves between cells thus making a master pattern.

Mandrake wrote:

JustMe wrote:Thanks that actually might help me!!! Though what I want is a bit different. The pattern in this wiki hexagon depends on the numbers in the cells but what I want to achieve is to make it depend on the moves between cells thus making a master pattern.

Probably something a mathematician can ponder on but, as maths was never my strong point, that counts me out !

Mandrake wrote:

JustMe wrote:Thanks that actually might help me!!! Though what I want is a bit different. The pattern in this wiki hexagon depends on the numbers in the cells but what I want to achieve is to make it depend on the moves between cells thus making a master pattern.

Probably something a mathematician can ponder on but, as maths was never my strong point, that counts me out !

Lawrence wrote:The mathematician in me wants to point out that your picture technically isn't a hexagon.

The magician in me wants to say it's probably in Fulves; it'll be in Fulves, yeah? It usually is