Unique Logic circuit grid.

[mfgoode]

An n x n square grid is said to be of order n when it has n^2 consecutive natural numbers and its magic constant is n(n^2 + 1 )/2.

Now take an order 3 grid and fill it in consecutive sequence from numbers 1 - 9 thus

1 2 3

4 5 6

7 8 9

Select any of the above numbers and circle it as a marker say the number
(3.)

Scratch out all numbers to the left of it, right of it, above and below it.

In this case the no.s (numbers) 1 , 2 and 6 and 9 are scratched out and cannot be further considered.

Now select any of the remaining no.s say (8) and scratch out as explained above.
The only remaining no. is 4 so circle it.

Now add the circled no.s. 3 + 8 + 4 = 15 the magic constant of the grid.

This process applies to any n x n grid and will always total to the M/constant .

This principle can be utilised practically in chip design, logic circuits, and a variety of industrial purposes.

This is an original contribution of mine and I expect this forum to protect my rights and interests in all matters concerned with this process.

Mally

[ewmayer]

This is completely trivial - if you'd bothered to do the simple proof of *why* the property holds you'd see that there's nothing whatsoever remarkable about it.

Originally Posted by mfgoode

This principle can be utilised practically in chip design, logic circuits, and a variety of industrial purposes.

How? I work in the field of digital programmable logic, and am well-versed in the algorithms used for logic placement and signal routing in programmable-logic devices. I see no possible relation between the trivial property of gridded sequences of natural numbers you describe and the challenges that arise e.g. in optimization problems related to digital logic layout (which I suspect you know zilch about.)

This is an original contribution of mine and I expect this forum to protect my rights and interests in all matters concerned with this process.

"Your contribution is both original and interesting. Unfortunately the part that is original is not interesting, and the part that is interesting is not original." But don't worry, I doubt you'll be seeing a lot of issues related to intellectual property theft on this one.

[victor]

Hmm. <nothing>
(Just thinking that if 1 is x and 9 x+8, the 'magic constant' is always x+12)

[ewmayer]

Victor, how was your recent move from Helvetistan to Switzerland? Did all your household furnishings survive intact? :P

[victor]

Originally Posted by ewmayer

Victor, how was your recent move from Helvetistan to Switzerland? Did all your household furnishings survive intact? :P

Well, I had to deal with Earth's gravity -- another 'magic constant'.
Besides that, everything's alright here in Switzerland .

(In fact, I tought Helvetistan was an ironic way of saying Switzerland, and I liked that. When I finally discovered what it was, I changed my profile (Helvetistan is the name given to the group of countries (Uzbekistan, Kyrgyzstan, Tajikistan, Turkmenistan, Azerbaijan and Poland) represented by Switzerland at the IMF and the World Bank.))

[mfgoode]

Originally Posted by victor

Hmm. <nothing>
(Just thinking that if 1 is x and 9 x+8, the 'magic constant' is always x+12)

So what? thats for only the order 3.
'magic constant' is an accepted and official term for magic squares and is widely used FYI.
I am talking about squares of order N whatever N's value is. The same principle holds for all values.

Mally

[mfgoode]

Originally Posted by ewmayer

This is completely trivial - if you'd bothered to do the simple proof of *why* the property holds you'd see that there's nothing whatsoever remarkable about it.

My mistake Herr ewmayer. I should have explained it better as you dont seem to have got the gist of it at all.

Originally Posted by ewmayer

How? I work in the field of digital programmable logic, and am well-versed in the algorithms used for logic placement and signal routing in programmable-logic devices.

How ? Try making a prime sieve out of it whose factors depend on addition and not division which is more difficult. If I knew I wouldn't bother posting it here. So I'm depending on you to work it out

[ QUOTE = ] I see no possible relation between the trivial property of gridded sequences of natural numbers you describe and the challenges that arise e.g. in optimization problems related to digital logic layout (which I suspect you know zilch about.)[/UNQUOTE]

Your suspicion is correct I know zilch about it. There's no shame in that is it?
If I knew digital logic layout You might be out of a job Herr Ernst !

Well in the old days you might remember the game 'Questions and Answers' which consisted of Questions on one half of the board and answers on the other half side.
There were two leads with pin jacks one of which could be inserted in a question socket. The other was inserted in the answer socket. If the answers were right (which were randomly placed ) the light bulb would only light up but not otherwise. As a child I managed to fathom out the circuit below the board. It was a simple connection from Ques. to answer and that would complete the cell circuit. Please think similarly for a fast electronic switching to sieve out the primes.

I see no possible relation between the trivial property of gridded sequences of natural numbers

Well Ernst, you did not see Hippocrates' solution in constructing the pieces into equal areas of the circle either! BTW I have given it a while ago.

[QUOTE =]"Your contribution is both original and interesting. Unfortunately the part that is original is not interesting, and the part that is interesting is not original." But don't worry, I doubt you'll be seeing a lot of issues related to intellectual property theft on this one.[/QUOTE]

Well! Well! Ernst a splendid play on words of 'discouragement'
Ridicule wont get you or me anywhere.
Yes I wont worry about intellectual property theft on this one. I have many more earth shaking theories to protect and I tell you I wont be relying on this forum. You may even be proud to have corresponded with me! But that is life
and the tide of fortune and fame.

So lets get back to work!

Mally