wonderboy1953
In Runtime
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- 195
Several things root
1) "ok, first, how do you think that your magic sqare (given in post 1) is semimagic? far from semi magic,it's magic fully (rows columns and diagonals all add to 34)
plus the corner 2x2 squares and the centre 2x2 adds to 34
plus it's pan diagonal..." If you had gone over what I posted more carefully, it's semimagic with respect to the secondary magic number of 85, not the primary magic number of 34 (btw the magic square I posted in post #1 is associative, not panmagic - doublecheck your work please).
2) "the intermediate squares don't all add up to 34, look at the intermediate square
on the left hand side:2+16+14+4 = 36, not 34 and the intermediate square on the right:13 + 3 + 1 + 15 = 32 again not 34; the square at the top centre
5+8+16+13 = 42 (not 34) and the middle centre square makes 4 + 1+9+12 = 26 (not 34)." Very good root except those aren't the intermediate squares. The intermediate squares (a - d) are:
a) 2 7 12 13
b) 3 6 9 16
c) 1 8 11 14
d) 4 5 10 15
If you draw lines between the numbers, you'll see that you get squares which are intermediate in size between the quadrant squares and the entire square depicted in post #1 on this thread.
3) " I think that the square that you want is:
12 06 15 01
13 03 10 08
02 16 05 11
07 09 04 14"
A panmagic square, root, very good except I wasn't looking for that square you found on the internet.
4) "with your square
11 05 08 10
02 16 13 03
14 04 01 15
07 09 12 06
I believe that what you want is...
11 x 1 + 5 X 2 + 8 + 3 + 10 * 4
11 + 10 + 24 + 40 = 85
and if you do that to all the rows you get a new (not) magic square where everything adds to 85 in the horizontal only. vertical columns are not adding to 85 so the square isn't magic?
11 10 24 40
02 34 39 12
14 08 03 60
07 18 36 24
and if you do the same with the verticals, then strangely the new vertical lines add to 85, but the horizontals don't (so again a not magic square, not even semi magic)
11 05 08 10
04 32 26 06
42 12 03 45
28 36 48 24
if I do the multiplication going backwards and forwards (11x1+5x2+8x3+10X4 next row 2x4+16x3+13x2+3x1 and so on)
11 10 24 40 = 85
08 48 26 03 = 85
14 08 03 60 = 85
28 27 24 06 = 85
I still don't get a magic square... (verticals break)
same things happen with the diagonals"
Root, you're slipping. When you dot multiply the rows and columns simultaneously by 1,2,3 and 4 (or reverse dot multiply simultaneously by 4,3,2 and 1), you get 85 as the answer for each row and column which makes this a semimagic square with respect to the secondary magic number of 85. This type of magic square that I discovered I designate as a bi-directional magic square because you get the same answer whether you dot multiply or reverse dot multiply (in this case 85). Now for my next puzzle which is to find an 8 x 8 magic square that's bi-directional with respect to dot multiplication and reverse dot multiplication by the numbers 1,2,3,4,5,6,7 and 8 (I've found six of them which are fully distinctive). Keep in mind root that I've done all of this work without the aid of a home computer which isn't going to help anybody to solve my second puzzle.
4) From post #28:
"What About Even Orders?
There is no known algorithm for generating even-order normal magic squares -- that is, normal magic squares where n is even." For the benefit of my reading audience, what root has stated isn't quite true. There are classes of even-ordered normal magic squares that do have "algorithms" for generation (I prefer to use the term methods). With respect to the 4 x 4 magic squares, I have methods that can easily transform one associative magic square into another associative magic square, a panmagic square into another panmagic square and a quadrant-associative magic square into another quadrant-associative magic square (hereafter shortened to the A, P and Q magic squares) plus I have bridge transform methods that can change an A square into a P or Q square and a P square into a Q square, or vice-versa.
That's about it. Oh one more thing root. Keep a bottle of Tylenol handy for your computer as it's going to wind up with one big headache when it tries to solve my second puzzle LOL (congratulations for solving my first puzzle as I wondered whether you had it in you).
1) "ok, first, how do you think that your magic sqare (given in post 1) is semimagic? far from semi magic,it's magic fully (rows columns and diagonals all add to 34)
plus the corner 2x2 squares and the centre 2x2 adds to 34
plus it's pan diagonal..." If you had gone over what I posted more carefully, it's semimagic with respect to the secondary magic number of 85, not the primary magic number of 34 (btw the magic square I posted in post #1 is associative, not panmagic - doublecheck your work please).
2) "the intermediate squares don't all add up to 34, look at the intermediate square
on the left hand side:2+16+14+4 = 36, not 34 and the intermediate square on the right:13 + 3 + 1 + 15 = 32 again not 34; the square at the top centre
5+8+16+13 = 42 (not 34) and the middle centre square makes 4 + 1+9+12 = 26 (not 34)." Very good root except those aren't the intermediate squares. The intermediate squares (a - d) are:
a) 2 7 12 13
b) 3 6 9 16
c) 1 8 11 14
d) 4 5 10 15
If you draw lines between the numbers, you'll see that you get squares which are intermediate in size between the quadrant squares and the entire square depicted in post #1 on this thread.
3) " I think that the square that you want is:
12 06 15 01
13 03 10 08
02 16 05 11
07 09 04 14"
A panmagic square, root, very good except I wasn't looking for that square you found on the internet.
4) "with your square
11 05 08 10
02 16 13 03
14 04 01 15
07 09 12 06
I believe that what you want is...
11 x 1 + 5 X 2 + 8 + 3 + 10 * 4
11 + 10 + 24 + 40 = 85
and if you do that to all the rows you get a new (not) magic square where everything adds to 85 in the horizontal only. vertical columns are not adding to 85 so the square isn't magic?
11 10 24 40
02 34 39 12
14 08 03 60
07 18 36 24
and if you do the same with the verticals, then strangely the new vertical lines add to 85, but the horizontals don't (so again a not magic square, not even semi magic)
11 05 08 10
04 32 26 06
42 12 03 45
28 36 48 24
if I do the multiplication going backwards and forwards (11x1+5x2+8x3+10X4 next row 2x4+16x3+13x2+3x1 and so on)
11 10 24 40 = 85
08 48 26 03 = 85
14 08 03 60 = 85
28 27 24 06 = 85
I still don't get a magic square... (verticals break)
same things happen with the diagonals"
Root, you're slipping. When you dot multiply the rows and columns simultaneously by 1,2,3 and 4 (or reverse dot multiply simultaneously by 4,3,2 and 1), you get 85 as the answer for each row and column which makes this a semimagic square with respect to the secondary magic number of 85. This type of magic square that I discovered I designate as a bi-directional magic square because you get the same answer whether you dot multiply or reverse dot multiply (in this case 85). Now for my next puzzle which is to find an 8 x 8 magic square that's bi-directional with respect to dot multiplication and reverse dot multiplication by the numbers 1,2,3,4,5,6,7 and 8 (I've found six of them which are fully distinctive). Keep in mind root that I've done all of this work without the aid of a home computer which isn't going to help anybody to solve my second puzzle.
4) From post #28:
"What About Even Orders?
There is no known algorithm for generating even-order normal magic squares -- that is, normal magic squares where n is even." For the benefit of my reading audience, what root has stated isn't quite true. There are classes of even-ordered normal magic squares that do have "algorithms" for generation (I prefer to use the term methods). With respect to the 4 x 4 magic squares, I have methods that can easily transform one associative magic square into another associative magic square, a panmagic square into another panmagic square and a quadrant-associative magic square into another quadrant-associative magic square (hereafter shortened to the A, P and Q magic squares) plus I have bridge transform methods that can change an A square into a P or Q square and a P square into a Q square, or vice-versa.
That's about it. Oh one more thing root. Keep a bottle of Tylenol handy for your computer as it's going to wind up with one big headache when it tries to solve my second puzzle LOL (congratulations for solving my first puzzle as I wondered whether you had it in you).