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#1 2007-10-10 16:14:07
- monicao
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- Registered: 2007-10-10
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a different magic square
Hy, I'm new here... I have to create a 6x6 magic square (sum of rows, colums, diagonals is the same). I have to use 1-once, 2-twice, 3-three times, 4-four times, 5 for five times and so on ... and 8 for eight times. I've tried many, many classic methods, but nothing worked... Any ideas, please? Thankyou!
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#2 2007-10-11 03:57:00
- Ricky
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- Registered: 2005-12-04
- Posts: 3,791
Re: a different magic square
What level of mathematics are you at? I could possibly see the use of an affine plane, but I'm not entirely sure how that would work out.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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#3 2007-10-11 06:09:02
- JaneFairfax
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- Registered: 2007-02-23
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Re: a different magic square
Well, the sum of all the numbers on the board is 1[sup]2[/sup]+2[sup]2[/sup]+
+8[sup]2[/sup] = 204, so the sum of each row/column must be 204⁄6 = 34. Thats the start Ive made so far. 
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#4 2007-10-11 07:01:06
- monicao
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- Registered: 2007-10-10
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Re: a different magic square
Thanks, Jane... I know this magic square is 34 sum... but I really can't build it...... HELPPPPPPPPPPPPP!!!!! Please....
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#5 2007-10-11 09:43:03
- MathsIsFun
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- Registered: 2005-01-21
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Re: a different magic square
Just a though: work out a symmetrical pattern for placing them (checkerboard may help).
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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#6 2007-10-11 12:00:29
- JaneFairfax
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- Registered: 2007-02-23
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Re: a different magic square
Symmetrical probably wont work. Ive tried. Since there are an odd number of each odd number, the leading diagonal must contain an odd number of each odd number in order for the board to be symmetrical. This will never produce a sum of 34 on the diagonal.
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#7 2007-10-11 12:39:08
- MathsIsFun
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Re: a different magic square
This one (has all odds):
1 3 5 7 = 16
3 3 5 7 = 18
5 5 5 7 = 22
7 7 7 7 = 28
Could maybe be compensated for with the evens?
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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#8 2007-10-11 18:53:50
- JaneFairfax
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- Registered: 2007-02-23
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Re: a different magic square
Did you get my drift? The sum of the leading diagonal must be 34. The sum of the diagonal entries in your mini-example is only 16. How are you going to make it 34 by adding only two more integers that are at most 8? 
Last edited by JaneFairfax (2007-10-11 18:55:57)
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#9 2007-10-11 20:49:03
- MathsIsFun
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Re: a different magic square
Quite right. Thought we should start somewhere.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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#10 2007-10-12 06:06:37
- John E. Franklin
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- Registered: 2005-08-29
- Posts: 3,588
Re: a different magic square
After moving 36
scraps of paper around
on a table for 3 hours, I
have an answer.
873376
386674
647467
258658
825748
785851
igloo myrtilles fourmis
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