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Ed_Millis![]() Inner circle Yuma, AZ 2292 Posts ![]() |
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![]() Special user St. Louis, MO 998 Posts ![]() |
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![]() Loyal user 291 Posts ![]() |
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.
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Ed_Millis![]() Inner circle Yuma, AZ 2292 Posts ![]() |
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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