Forums / Miscellaneous Discussions / Help with Magic Square

Help with Magic Square
21:39:54 May 28th 08 - Duke Argyle:

I got this problem from a girl in 8th grade, I said it was impossible to solve because I didn't want to appear stupid since I couldn't find out the answer. Now, anyone familiar with this kind of problem?

The sum of all rows, vertical, linear and diagonal is the same, read up on Magic Square


7 X X
X 15 X
5 X X

Any number is ok to use.


21:54:05 May 28th 08 - Mr. Killer:

15 > 7+5

15+X > 7+5+X

So, unless we're allowed use negatives?

21:59:02 May 28th 08 - Duke Argyle:

is negative numbers any number? :P I can only assume it's ok.


22:06:31 May 28th 08 - Mr. Killer:

I've never seen a magic square with a negative number.


22:26:22 May 28th 08 - Mr. Pedro Al Bear:

Also most magic squares have values from that vary from 1 to n^2 where n is the number of rows, in your care n=3, so the values can only be between 1 to 9. What you have here is not your run of the mill magic square, or you just got the numbers wrong.


22:28:40 May 28th 08 - Mr. Ironic:

Negative numbers anyone?


22:30:45 May 28th 08 - Mr. Pedro Al Bear:

I have never seen a Magic Square with negative numbers, as far as I know it can only have positive ones.


22:31:59 May 28th 08 - Mr. Ant:

well if all the numbers are negative its ok


22:44:23 May 28th 08 - Mr. Pedro Al Bear:

If all numbers are negative it wouldn't really matter, they might just as well be positive. Ant do you post just because you like to see your post count rise on the kingdom page?


22:48:28 May 28th 08 - Mr. Ant:

no i just like to annoy you, lol,

I know they would just as well be positive, hence how i could say they could all be negative


23:03:25 May 28th 08 - Mr. Pedro Al Bear:

You're a *beep* aren't you?


23:11:36 May 28th 08 - Mr. Ant:

a what?


23:46:31 May 28th 08 - Mr. Jones:

7  a  b
c 15 d
5  e  f


d = -3 since d = 7+5-15
b = 25 since b + d + f = 7 + 15 + f
thus each row, column and diagonal equals 45 (also 3 times the middle square)
f = 23 since 7 + 15 + f = 45
c = 33 since 7 + c + 5 = 45
a = 13 since 7 + a + b = 45
e = 17 since 5 + e + f = 45

therefore the square is

7 - 13 - 25
33 - 15 - (-3)
5 - 17 - 23


00:38:34 May 29th 08 - Mr. Ironic:

We already knew this but the problem is that it uses a negative number.  So it's technically not a real magic square.


02:17:04 May 29th 08 - Duke Argyle:

it's an arbitrary magic square, let's say the teacher was unaware of the regulations. And to be clear, there is no rules the numbers must be 1-9.

thank you Jones :D


07:56:10 May 29th 08 - Mr. Pedro Al Bear:

I said standard magic squares ...

"A normal magic square contains the integers from 1 to n."

From your own link, there do exist nonstandard magic squares that do not have the above rule.


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