Math question (semi-simple)

[wonderboy1953]

Several things root

1) "ok, first, how do you think that your magic sqare (given in post 1) is semimagic? far from semi magic,it's magic fully (rows columns and diagonals all add to 34)
plus the corner 2x2 squares and the centre 2x2 adds to 34
plus it's pan diagonal..." If you had gone over what I posted more carefully, it's semimagic with respect to the secondary magic number of 85, not the primary magic number of 34 (btw the magic square I posted in post #1 is associative, not panmagic - doublecheck your work please).

2) "the intermediate squares don't all add up to 34, look at the intermediate square
on the left hand side:2+16+14+4 = 36, not 34 and the intermediate square on the right:13 + 3 + 1 + 15 = 32 again not 34; the square at the top centre
5+8+16+13 = 42 (not 34) and the middle centre square makes 4 + 1+9+12 = 26 (not 34)." Very good root except those aren't the intermediate squares. The intermediate squares (a - d) are:

a) 2 7 12 13
b) 3 6 9 16
c) 1 8 11 14
d) 4 5 10 15

If you draw lines between the numbers, you'll see that you get squares which are intermediate in size between the quadrant squares and the entire square depicted in post #1 on this thread.

3) " I think that the square that you want is:

12 06 15 01
13 03 10 08
02 16 05 11
07 09 04 14"

A panmagic square, root, very good except I wasn't looking for that square you found on the internet.

4) "with your square

11 05 08 10
02 16 13 03
14 04 01 15
07 09 12 06


I believe that what you want is...

11 x 1 + 5 X 2 + 8 + 3 + 10 * 4
11 + 10 + 24 + 40 = 85

and if you do that to all the rows you get a new (not) magic square where everything adds to 85 in the horizontal only. vertical columns are not adding to 85 so the square isn't magic?


11 10 24 40
02 34 39 12
14 08 03 60
07 18 36 24

and if you do the same with the verticals, then strangely the new vertical lines add to 85, but the horizontals don't (so again a not magic square, not even semi magic)

11 05 08 10
04 32 26 06
42 12 03 45
28 36 48 24


if I do the multiplication going backwards and forwards (11x1+5x2+8x3+10X4 next row 2x4+16x3+13x2+3x1 and so on)

11 10 24 40 = 85
08 48 26 03 = 85
14 08 03 60 = 85
28 27 24 06 = 85

I still don't get a magic square... (verticals break)
same things happen with the diagonals"

Root, you're slipping. When you dot multiply the rows and columns simultaneously by 1,2,3 and 4 (or reverse dot multiply simultaneously by 4,3,2 and 1), you get 85 as the answer for each row and column which makes this a semimagic square with respect to the secondary magic number of 85. This type of magic square that I discovered I designate as a bi-directional magic square because you get the same answer whether you dot multiply or reverse dot multiply (in this case 85). Now for my next puzzle which is to find an 8 x 8 magic square that's bi-directional with respect to dot multiplication and reverse dot multiplication by the numbers 1,2,3,4,5,6,7 and 8 (I've found six of them which are fully distinctive). Keep in mind root that I've done all of this work without the aid of a home computer which isn't going to help anybody to solve my second puzzle.


4) From post #28:

"What About Even Orders?
There is no known algorithm for generating even-order normal magic squares -- that is, normal magic squares where n is even." For the benefit of my reading audience, what root has stated isn't quite true. There are classes of even-ordered normal magic squares that do have "algorithms" for generation (I prefer to use the term methods). With respect to the 4 x 4 magic squares, I have methods that can easily transform one associative magic square into another associative magic square, a panmagic square into another panmagic square and a quadrant-associative magic square into another quadrant-associative magic square (hereafter shortened to the A, P and Q magic squares) plus I have bridge transform methods that can change an A square into a P or Q square and a P square into a Q square, or vice-versa.

That's about it. Oh one more thing root. Keep a bottle of Tylenol handy for your computer as it's going to wind up with one big headache when it tries to solve my second puzzle LOL (congratulations for solving my first puzzle as I wondered whether you had it in you).

 

[wonderboy1953]

Being fair to root

About two years ago I was at the same level as root was when it came to my knowledge on magic squares where I looked up information or read books as well as my own personal study on them. Eventually I became very good at them through practice and study.

Root isn't the first person to make mistakes. I have books that have made mistakes, e.g. I have one that said the Benjamin Franklin square is a magic square explicitly saying that the diagonals also summed up to 260 when such is not the case (the 8 x 8 square is semimagic with respect to the rows and columns). At least root took a stab at it (with the help of my hints) which no one else did.

I've only scratched the surface with magic squares. There is so much I haven't covered
which, if someone is interested, I'll do more posting on. In the meantime I posted another puzzle which I'll await for someone to post an answer to.

Good luck.

 

[JogaBonito1502]

Since we're being brutally honest as far as our accomplishments go, I would like to defend myself by saying that I didn't become thoroughly involved in this thread because magic squares have no use in my life, EVER. Coming out and implicitly saying that you're the best with magic squares, congratulating Root for taking a side in a argument that you're declaring yourself the winner by imposing your presumably superior knowledge of magic squares, and further assuming that Root would not have come to his conclusion without the aid of your "hints" is very disrespectful. It may be just circumstances of my day that affect my feeling regarding this post, but I find it extremely offensive to just assume someone is not as capable as you in such explicit language. I generally try to comprehend a person's intentions as positively as I can conjure it up, however I found this post absurd. I do not doubt that you are a very capable mathematician, especially when it comes to the curiosity of magic squares, but in the future refrain from making such extreme claim. You show good humility in accessing the depth of information you've uncovered about magic squares, but the first two paragraphs I found outrageous.

Why should you care about what I just said? Part of being a good member is to be respectful to your peers. Considering you current standing in this forum (with regards to negative reputation), I would try to be more crafty on how posts are worded. This is no threat, just a heads up.

 

[root]

Re: Several things root

it's rare that I ever pull someone up on the use of forum software, because i realise not everyone spends as much time on forums perhaps as much as I do.

but I really suggest that when you are replying to someone that you use the quote tags, it'll make your end post a lot easier to read and understand what you're writing and what other people have written.

If you had gone over what I posted more carefully, it's semimagic with respect to the secondary magic number of 85, not the primary magic number of 34 (btw the magic square I posted in post #1 is associative, not panmagic - doublecheck your work please).

firstly, you said with respect to the semi-magic square of post 1. the square in post 1 isn't only semi magic... I didn't work it wrong in that respect, your post was ambiguous... perhaps you should have double checked your wording before my working.

secondly, I didn't say, pan magic, I said pan diagonal, there is a difference in meaning between the two seperate words. (one can only imagine that's why there are two different words to describe the two different things).

I believe that what you want is...

I had to write I believe what you want is, because you never actually posted a concise problem, you vaguely said that you'd found something interesting, said number 85 is important and asked us to relate numbers 1234 to the square to guess what you are thinking...

When you dot multiply the rows and columns simultaneously by 1,2,3 and 4 (or reverse dot multiply simultaneously by 4,3,2 and 1),

I'm still having touble understanding what you mean, can you post your resultant square after the dot multiplication?
please show your working.

Keep in mind root that I've done all of this work without the aid of a home computer.

I sat down with a notepad in my lunch hour, I don't have any tools installed on my computer... your point is?

"What About Even Orders?
There is no known algorithm for generating even-order normal magic squares -- that is, normal magic squares where n is even." For the benefit of my reading audience, what root has stated isn't quite true. There are classes of even-ordered normal magic squares that do have "algorithms" for generation (I prefer to use the term methods).

you don't seem to get what I mean...
an algorithm for generating magic squares would be something something that can be expressed in terms of n sides, possibly generating a number when given n sides for the number in a sequence from z=1 >= z=n*n in terms of their position in x and y...

Since we're being brutally honest as far as our accomplishments go, I would like to defend myself by saying that I didn't become thoroughly involved in this thread because magic squares have no use in my life,

Mine either, I've spent most of my posts in this thread asking for a useful purpose for magic squares, still yet to hear one...

About two years ago I was at the same level as root was when it came to my knowledge on magic squares where I looked up information or read books as well as my own personal study on them. Eventually I became very good at them through practice and study.

if that's serious then there's no doubting that you've made an achievement there...

perhaps you find these magic squares really interesting, but to go from the level of knowing nothing, to apparently knowing so much. (and I really don't mean to sound like a cock but...) just imagine what you could have accomplished had you decided to study something with a purpose!

anyway...

I'm still confused about your first problem,
can you post the square that you get after your simultaneous dot multiplication?

 

[wonderboy1953]

Several more things root

it's rare that I ever pull someone up on the use of forum software, because i realise not everyone spends as much time on forums perhaps as much as I do.

but I really suggest that when you are replying to someone that you use the quote tags, it'll make your end post a lot easier to read and understand what you're writing and what other people have written.

firstly, you said with respect to the semi-magic square of post 1. the square in post 1 isn't only semi magic... I didn't work it wrong in that respect, your post was ambiguous... perhaps you should have double checked your wording before my working.

secondly, I didn't say, pan magic, I said pan diagonal, there is a difference in meaning between the two seperate words. (one can only imagine that's why there are two different words to describe the two different things).


I had to write I believe what you want is, because you never actually posted a concise problem, you vaguely said that you'd found something interesting, said number 85 is important and asked us to relate numbers 1234 to the square to guess what you are thinking...


I'm still having touble understanding what you mean, can you post your resultant square after the dot multiplication?
please show your working.

I sat down with a notepad in my lunch hour, I don't have any tools installed on my computer... your point is?


you don't seem to get what I mean...
an algorithm for generating magic squares would be something something that can be expressed in terms of n sides, possibly generating a number when given n sides for the number in a sequence from z=1 >= z=n*n in terms of their position in x and y...

Mine either, I've spent most of my posts in this thread asking for a useful purpose for magic squares, still yet to hear one...

if that's serious then there's no doubting that you've made an achievement there...

perhaps you find these magic squares really interesting, but to go from the level of knowing nothing, to apparently knowing so much. (and I really don't mean to sound like a cock but...) just imagine what you could have accomplished had you decided to study something with a purpose!

anyway...

I'm still confused about your first problem,
can you post the square that you get after your simultaneous dot multiplication?

1) "secondly, I didn't say, pan magic, I said pan diagonal, there is a difference in meaning between the two seperate words."
Oh really root? Maybe you won't take my word for it that they ARE the same. E.g. check out Magic Squares Glossary where it says:

Pan-Diagonal: A Magic Square in which all the broken daigonals also sum to magic sum. See also Pan-Magic and Nasik Pan-Magic Square

Pan-Magic Square: A Magic Square in which all the broken daigonals also sum to the magic sum. See also Pan-Diagnonal and Nasik

2) "I'm still having touble understanding what you mean, can you post your resultant square after the dot multiplication?
please show your working."

With respect to dot multiplication, you actually know what it is root as you did the work of posting. Here's what you posted:

"I believe that what you want is...

11 x 1 + 5 X 2 + 8 + 3 + 10 * 4
11 + 10 + 24 + 40 = 85

and if you do that to all the rows you get a new (not)magic square where everything adds to 85 in the horizontal only. vertical columns are not adding to 85 so the square isn't magic?" (by accident you put in the addition sign instead of the multiplication sign between 8 and 3 above)

More formally, dot multiplication relates to the dot product which emphasizes the end result while dot multiplication emphasizes the process itself towards getting to the result.

The square I posted in post #1 is both a magic square and a semimagic square too.

The following demonstrates the bi-directionality of the square (and also shows dot multiplication for the rows which equals 85):

11 x 1 + 5 X 2 + 8 x 3 + 10 x 4 = 2 x 1 + 16 x 2 + 13 x 3 + 3 x 4 = 14 x 1 + 4 x 2 + 3 x 1 + 15 x 4 = 7 x 1 + 9 x 2 + 12 x 3 + 6 x 4 = 85 which are the rows dot multiplied by 1,2,3 and 4.

11 x 4 + 5 x 3 + 8 x 2 + 10 x 1 = 2 x 4 + 16 x 3 + 13 x 2 + 3 x 1 = 14 x 4 + 4 x 3 +
3 x 2 + 15 x 1 = 7 x 4 + 9 x 3 + 12 x 2 + 6 x 1 = 85 which are the rows reversed dot multiplied by 4,3,2 and 1.

By what you've said and done previously and what I just did, you should have no problem in dot multiplying and reverse dot multiplying the columns to get 85 again.

This should be enough to answer your main concerns. Now regarding JogaBonito1502:

"Originally Posted by JogaBonito1502 View Post
Since we're being brutally honest as far as our accomplishments go, I would like to defend myself by saying that I didn't become thoroughly involved in this thread because magic squares have no use in my life," Then why are you "thoroughly involved in this thread?"

 

[root]

Re: Several more things root

Pan-Diagonal: A Magic Square in which all the broken daigonals also sum to magic sum. See also Pan-Magic and Nasik Pan-Magic Square

Pan-Magic Square: A Magic Square in which all the broken daigonals also sum to the magic sum. See also Pan-Diagnonal and Nasik

what I read (on a different site) was that a pan diagonal square was one where:
it was magic, (eg horizontal and verticals all summed the same)
and that all diagonals (including broken diagonals).

in other words a pan diagonal square may be magic in the usual way, whilst also being magic in all diagonal ways... but not necessarily have other properties

whilst a pan magic way would have to be magic in all ways, (vertical, horizontal, diagonal, broken diagonal, quadrant, centre intermediate and wrapped squares and corners (like the square that I posted).

magic in every way, completely magic, or pan magic. from the ancient geek pan

pan-, pant(o)- Denoting something as 'complete' or containing 'everything' Ancient Greek πᾶς, παν- (pas, pan-), all, every

which as I said, made your square magic in several ways but not all, (hence why I said pan diagonal [complete diagonal magic] whilst mine was pan magic [completely magic in every possible way]).

but if you say that your definition is different then that's fine, but doesn't seem to work as far as I understand how language works...

2) "I'm still having touble understanding what you mean, can you post your resultant square after the dot multiplication?
please show your working."

With respect to dot multiplication, you actually know what it is root as you did the work of posting. Here's what you posted:

actually, no, that's the point, I don't understand.

though now that you posted that I understand a little better

you say that you can produce a semi magic square, but frankly you can't not even vaguely, you can multiply in one direction 1234 or 4321 and get a not magic square, or you can multiply the verticals and still get a not magic square...


yes, it's pretty cool that multiplying forwards or backwards get's you 85, but frankly the rest of "your discovery" is complete bollocks.
you can't simultaneously multiple things in the way that you're trying to.

basically, you can multiply the numbers in your magic square to get two squares of numbers which have no real useful properties at all.


if I do math the same way as you do, (as in make it up as I go along) then I'm sure that I can make some amazing discoveries too.

but just like your amazing discovery, they'll be near impossibly to explain to anyone who doesn't have the same retardations as myself, and frankly a complete load of old bollocks...

you can't show your working because your processes are impossible.
you can't produce a single magic square (as you said that you could)
because there is no magic square, (or semi magic squares) just two (or four) completely not magic squares.

you said come up with a new semi magic square. but you can't even do that!

no wonder I found it so hard to follow you. you're spouting complete bollocks.

if you think that you're not then prove me wrong:

take your magic square from post 1, relate to the numbers 1,2,3,4 and come up with a semi magic square where the produce is 85.

I'll bet you can't. even after all your years of study and self proclaimed genius...
suddenly I don't feel too shabby that I couldn't figure it out either...

More formally, dot multiplication relates to the dot product which emphasizes the end result while dot multiplication emphasizes the process itself towards getting to the result.

did you mistype something?

are you trying to make this as clear as mud or what?

 

[wonderboy1953]

Re: Several more things root

what I read (on a different site) was that a pan diagonal square was one where:
it was magic, (eg horizontal and verticals all summed the same)
and that all diagonals (including broken diagonals).

in other words a pan diagonal square may be magic in the usual way, whilst also being magic in all diagonal ways... but not necessarily have other properties

whilst a pan magic way would have to be magic in all ways, (vertical, horizontal, diagonal, broken diagonal, quadrant, centre intermediate and wrapped squares and corners (like the square that I posted).

magic in every way, completely magic, or pan magic. from the ancient geek pan



which as I said, made your square magic in several ways but not all, (hence why I said pan diagonal [complete diagonal magic] whilst mine was pan magic [completely magic in every possible way]).

but if you say that your definition is different then that's fine, but doesn't seem to work as far as I understand how language works...


actually, no, that's the point, I don't understand.

though now that you posted that I understand a little better

you say that you can produce a semi magic square, but frankly you can't not even vaguely, you can multiply in one direction 1234 or 4321 and get a not magic square, or you can multiply the verticals and still get a not magic square...


yes, it's pretty cool that multiplying forwards or backwards get's you 85, but frankly the rest of "your discovery" is complete bollocks.
you can't simultaneously multiple things in the way that you're trying to.

basically, you can multiply the numbers in your magic square to get two squares of numbers which have no real useful properties at all.


if I do math the same way as you do, (as in make it up as I go along) then I'm sure that I can make some amazing discoveries too.

but just like your amazing discovery, they'll be near impossibly to explain to anyone who doesn't have the same retardations as myself, and frankly a complete load of old bollocks...

you can't show your working because your processes are impossible.
you can't produce a single magic square (as you said that you could)
because there is no magic square, (or semi magic squares) just two (or four) completely not magic squares.

you said come up with a new semi magic square. but you can't even do that!

no wonder I found it so hard to follow you. you're spouting complete bollocks.

if you think that you're not then prove me wrong:

take your magic square from post 1, relate to the numbers 1,2,3,4 and come up with a semi magic square where the produce is 85.

I'll bet you can't. even after all your years of study and self proclaimed genius...
suddenly I don't feel too shabby that I couldn't figure it out either...


did you mistype something?

are you trying to make this as clear as mud or what?

"you can't simultaneously multiple things in the way that you're trying to." To use your disgusting term, bollocks, because it is true as I demonstrated.

"if I do math the same way as you do, (as in make it up as I go along) then I'm sure that I can make some amazing discoveries too." "(as in make it up as I go along)", again bollocks. Well I don't expect you to make amazing discoveries in math because it isn't useful to you.

"but just like your amazing discovery, they'll be near impossibly to explain to anyone who doesn't have the same retardations as myself, and frankly a complete load of old bollocks..." Here you're contradicting yourself because where did you come up with my discovery being amazing?

"you can't show your working because your processes are impossible." for someone who just said "they'll be near impossibly to explain to anyone who doesn't have the same retardations as myself" is again being contradictory. Anyways how would you know that the "processes are impossible?" What processes are you referring to and where's your proof?

To sum it up I think you're trying to play me into thinking that you're a fool. I'm sure you really do understand. So I turn to others who've been following this thread and ask for your input. And if I hear from others (not counting root) that you need some hints towards a solution, that is an 8 x 8 magic square that's also semimagic, just post onto this thread and I'll be happy to comply.

Root subsequently posted this: "but this simultaneous dot product multiplication is just a pure fantasy. it is an impossible process, you haven't demonstrated it at all you can't do it. (because it's impossible)" Those equal signs are not in your favor root.

 

[root]

I do understand what you did. (after you explained what you did)

you multiplied along the rows (first number by 1, second number by 2 etc) and made a square with a sum of 85 for all the rows.
you then multiplied by all the columns to make a different square where the sum of all the columns is 85.

as I said that is pretty cool... especially as it doesn't matter which way round you multiply. (first number by 4, second number by 3 etc)

but this simultaneous dot product multiplication is just a pure fantasy. it is an impossible process, you haven't demonstrated it at all
you can't do it. (because it's impossible)

and that's exactly why you can't draw your "semi magic square", because there is no semi magic squares, just two regular squares with no real useful of spectacular properties at all.
and that's exactly why you haven't invented a bi-magic anything, because your process is flawed.

your process is impossible my proof being that it can't be done. (besides that, it's up to you to prove that your process works. I know that you can't because it doesn't), but when you come up with a process, you need to explain, and prove the process. maths and science don't work like religion.

whilst you're pointing out contradictions... can you explain this one?

More formally, dot multiplication relates to the dot product which emphasizes the end result while dot multiplication emphasizes the process itself towards getting to the result.

(on a side note, this post is bereft of sarcasm since you weren't able to decide what was and was no sarcasm in my last post.)

also, I'm not trying to make you think I'm a fool I'm just trying to get some sense out of you.

so far you've had trouble writing the problem, trouble reading the posts in the thread, now you appear to be having trouble with basic arithmetic...

I'm starting to wonder if this basic trouble with the "three R's" is you trying to act like a fool...

edit -

if there is anyone left reading this post that thinks that this simultaneous multiplication thing is real then can they please explain,

obviously comp_explorer is having trouble explaining it to me.
or I'm having trouble understanding it. and just like the three doors puzzle I'd quite like to learn something new... (and it's often just in the way that it's explained that makes the difference).

 

[wonderboy1953]

Root is putting the cart before the horse

I didn't ask for anyone to show me a semimagic square as I already put it up on this thread (in post #1). What I did ask for was to show why it was so special (the square in post #1 which root unwittingly did when he showed that dot multiplying by 1,2,3,4 resulted in 85 for all the rows and columns).

That square in post #1 is the only magic square that yields the same result (85) upon dot multiplication and reverse dot multiplication on all its rows and columns. The other 879 4 x 4 magic squares don't have that property. E.g. try dot multiplying the rows and columns in the following magic square by 1,2,3 and 4:

16 02 03 13
05 11 10 08
09 07 06 12
04 14 15 01

and see what results (again root, I'm not looking for a square, just for the results
of dot multiplying the rows and columns of that square).

So what I'm saying is the square from post #1 is both magic (since its rows, columns
and diagonals add up to the magic sum of 34, its first magic number) and semimagic (since its rows and columns yield the same number, 85, upon dot multiplication by 1,2,3 and 4, which is its secondary magic number).

It's nice to know too the square is bi-directional since dot multiplication and reverse
dot multiplication yields the same result for all rows and columns (while we're on this discussion, try dot multiplying by 2,3,4 and 5 or 1,4,7 and 10 to see what happens also try dot multiplying and reverse dot multiplying by the oblong numbers; 2,6,12 and 20 and the triangle numbers 1,3,6 and 10 to see further what happens).

In regards to the sarcasm, I take it to mean the term "bollocks" you had been using.
The term is profane and has negative connotations which I find offensive. The term
"nonsense" would serve you much better on my threads.

Now that you know what is meant by a bi-directional square whose rows and columns are semimagic and yield the same result after dot multiplying and reverse dot multiplying, again I pose the same challenge: can you find an 8 x 8 magic square
that is also semimagic and bi-directional in the same manner as the square from post #1? (with respect to the numbers 1,2,3,4,5,6,7 and 8; also what is its secondary magic number?)

 

[berry120]

In regards to the sarcasm, I take it to mean the term "bollocks" you had been using.
The term is profane and has negative connotations which I find offensive. The term
"nonsense" would serve you much better on my threads.

Your threads? Serve you much better? If you find it offensive, ignore it. Or write a greasemonkey script to replace all swear words with innocent counterparts.

You're possibly in the worst place ever known on these forums to tell a moderator (of all people) what language he can and can't use. If you don't like it, stop posting.