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The Magic Cafe Forum Index » » Magical equations » » List of all solutions for Durer's magic square? (0 Likes) Printer Friendly Version

Ed_Millis
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Inner circle
Yuma, AZ
2292 Posts

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I saw an article on Durer's magic square that claimed 86 ways to get 34. Try as I might, I can only find 32. I have a presentation that would be enhanced if I could show 34 ways to get 34.

Can anyone provide or point me to a resource that would show at least 34 solutions?

Ed
stanalger
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St. Louis, MO
998 Posts

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Don't use Dürer's magic square. It's not magic enough.
Here's one of the type you seek:
1st row: 4, 5, 16, 9
2nd row: 14, 11, 2, 7
3rd row: 1, 8, 13, 12
4th row: 15, 10, 3, 6

You can get a total of 34 in at least 52 different, nice, symmetric ways!

Here's a partial list:

4 rows
4 columns
8 diagonals (includes "broken" diagonals)
9 2x2 squares

The four corners of each of the following rectangles:

1 4x4 square
3 2x4 rectangles
3 4x2 rectangles
4 3x3 squares

See Sam Dalal's "Patterns of Perfection" for a more complete list.

Al Stanger
fyi2
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Loyal user
291 Posts

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Just got 'Sam Dalal's "Patterns of Perfection" for a more complete list', very good book, well worth the $5. You can find it in Lybra.
Ed_Millis
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Yuma, AZ
2292 Posts

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I eventually did manage to find 34 patterns for Durer's Square.
(Not that I'm opposed to using others - I just wanted to work at this one first.)

4 rows
4 columns
2 diagonals
1 corners
1 corners, rotated once CW
1 corners, rotated once CCW
7 2x2 squares
4 3x3 squares (corners)
4 "kites" (ie: 5,3,11,15)
(only works vertically, but
both up and down)
2 diagonal pairs
(5,3,14,12 and 9,15,2,8)
4 "zig zag" from each corner
(ie: 16,8,9,1)

And thank you for the reference to Sam Dalal's "Patterns of Perfection".
I will be checking that out soon!

Ed
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