Math Is Fun Forum

gyanshrestha

Member

Registered: 2007-11-06

Posts: 41

magic square

can anyone help me to fill out the magic square of 9 by 9 with the given series.
1+3+5+7+....................

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http://gyan.talkacademy.com.np

NullRoot

Member

Registered: 2007-11-19

Posts: 162

Re: magic square

You're using every odd number, right? Here you go:

093    115    137    159    001    023    045    067    089
113    135    157    017    021    043    065    087    091
133    155    015    019    041    063    085    107    111
153    013    035    039    061    083    105    109    131
011    033    037    059    081    103    125    129    151
031    053    057    079    101    123    127    149    009
051    055    077    099    121    143    147    007    029
071    075    097    119    141    145    005    027    049
073    095    117    139    161    003    025    047    069

It all adds up to 729.

There's an algorithm I know for doing this and it worked for the odd numbers luckily.

1. The first number goes in the middle cell of the top row.
2. Place the next number 1 right and 1 up from that number (the order of this is important).
     2.a If you're at the right-most cell when you try to move right, go to the left most cell of the same row instead.
     2.b If you're at the top most cell when you try to move up, then go to the bottom of the current column instead.
3. If the destination cell is already populated, then fill in the cell 1 down from the last one you filled in instead.
4. Repeat until you've filled in the whole thing.

It should work for any magic square with odd-dimensions.

Last edited by NullRoot (2007-12-05 23:43:41)

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Trillian: Five to one against and falling. Four to one against and falling… Three to one, two, one. Probability factor of one to one. We have normality. I repeat, we have normality. Anything you still can’t cope with is therefore your own problem.

gyanshrestha

Member

Registered: 2007-11-06

Posts: 41

Re: magic square

thanks
and whats for 8 by 8 magic square.

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http://gyan.talkacademy.com.np

NullRoot

Member

Registered: 2007-11-19

Posts: 162

Re: magic square

Good question. I don't know the even-square algorithm

Edit: I'd probably fall back on 17 simultaneous equations

Last edited by NullRoot (2007-12-07 00:35:33)

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Trillian: Five to one against and falling. Four to one against and falling… Three to one, two, one. Probability factor of one to one. We have normality. I repeat, we have normality. Anything you still can’t cope with is therefore your own problem.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: magic square

Apparently you can double and add constants to magic square numbers.
1,2,3,4,5 goes to 2,4,6,8.10, and then minus 1 to get odds 1,3,5,7,9.
Very interesting indeed, since odd numbers stem from -1, and
even numbers stem from 0 (the missing number before the series)

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