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lakelady
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 Posted: Thu Aug 25, 2005 3:37 am Post subject: diagonal rows |
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| we are new to this game and were wondering if beside the vertical and horizonal lines and the 3x3 cubes, if you need to worry about the diagonal numbers also? |
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ForestStryfe
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| Posted: Thu Aug 25, 2005 3:55 pm Post subject: |
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| No, you do not need to look at diagonal lines. |
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someone_somewhere
Joined: 07 Aug 2005
Posts: 275
Location: Munich
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| Posted: Fri Aug 26, 2005 7:58 am Post subject: |
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Hi,
It would be an additional "beauty" of a position that has all the numbers from 1 to 9 on both diagonals.
For a barrel of whisky, I could find you, such a nice one.
see u, |
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mars15
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| Posted: Wed Jan 18, 2006 3:06 am Post subject: Re: diagonal rows |
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| lakelady wrote: | | we are new to this game and were wondering if beside the vertical and horizonal lines and the 3x3 cubes, if you need to worry about the diagonal numbers also? |
People like Sudoku because it is easy to solve. If you really want to see the real magic square of
order 9, you shouldn't neglect the 9x9 panmagic square, one example shows as follow:
1 42 76 9 38 75 5 43 80
50 61 17 46 60 13 54 56 12
36 65 21 32 70 26 28 69 22
73 6 40 81 2 39 77 7 44
14 52 62 10 51 58 18 47 57
27 29 66 23 34 71 19 33 67
37 78 4 45 74 3 41 79 8
59 16 53 55 15 49 63 11 48
72 20 30 68 25 35 64 24 31
9 Rows: Sum(1,42,76,9,38,75,5,43,80)=369
9 Columns:Sum(1,50,36,73,14,27,37,59,72)=369
2 Diagonals:Sum(1,61,21,81,51,71,41,11,31)=369
16 Broken diagonals:Sum(43,54,26,2,10,66,78,59,31)=369
9 3x3Blocks:Sum(1,42,76,50,61,17,36,65,21)=369
Any 3x3 Block:Sum(61,65,6,17,21,40,46,32,81)=369
Any 3x3 Broken block:Sum(42,1,80,61,50,12,72,20,31)=369
The form of Sudogu
01 06 04 09 02 03 05 07 08 Row meets the rule.
05 07 08 01 06 04 09 02 03
09 02 03 05 07 08 01 06 04
01 06 04 09 02 03 05 07 08
05 07 08 01 06 04 09 02 03
09 02 03 05 07 08 01 06 04
01 06 04 09 02 03 05 07 08
05 07 08 01 06 04 09 02 03
09 02 03 05 07 08 01 06 04
Column does not meet the rule, but diagonal meets the rule.
Any 3x3 Block meets the rule.
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mars15
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| Posted: Wed Jan 18, 2006 3:45 am Post subject: Sudoku and magic square |
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Another 9x9 panmagic square's example completely meets the rule of Sudoku showing as follow:
37 47 79 60 67 12 26 9 32 369
3 35 45 50 73 56 70 15 22 369
11 25 6 31 39 53 81 59 64 369
62 72 14 19 2 34 42 49 75 369
52 78 58 66 17 27 5 28 38 369
36 41 46 74 61 69 13 21 8 369
24 4 30 44 54 77 55 65 16 369
68 10 20 7 33 40 48 80 63 369
76 57 71 18 23 1 29 43 51 369
9 Rows: Sum(37,47,79,60,67,12,26,9,32)=369
9 Columns:Sum(37,3,11,62,52,36,24,68,76)=369
2 Main diagonals:Sum(37,35,6,19,17,69,55,80,51)=369
16 Broken diagonals:Sum(62,25,45,60,23,40,55,21,3 =369
The form of Sudogu:
1 2 7 6 4 3 8 9 5 Row meets the rule.
3 8 9 5 1 2 7 6 4
2 7 6 4 3 8 9 5 1
8 9 5 1 2 7 6 4 3
7 6 4 3 8 9 5 1 2
9 5 1 2 7 6 4 3 8
6 4 3 8 9 5 1 2 7
5 1 2 7 6 4 3 8 9
4 3 8 9 5 1 2 7 6
Column meets the rule too. Some diagonals (///) also meet the rule.
9- 3x3 Block meets the rule.
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mars15
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| Posted: Wed Jan 18, 2006 5:19 pm Post subject: The most beautiful Sudoku |
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The most "beautiful" Sudoku is based on the 9x9 bimagic square, 9 rows, 9 columns, and 2 nain
diagonals (actually also include 4-broken diagonals) meet the Sudoku rule, and magic sum 369,
"square" sum 20049.
This 9x9 biamagic square's example completely meet the rule of Sudoku showing as follow:
37 18 68 35 4 57 51 20 79
2 61 33 27 77 46 13 66 44
75 53 22 70 42 11 59 28 9
58 30 8 74 52 24 72 41 10
50 19 81 39 17 67 34 6 56
15 65 43 1 63 32 26 76 48
25 78 47 14 64 45 3 62 31
71 40 12 60 29 7 73 54 23
36 5 55 49 21 80 38 16 69
9 Rows: Sum(37,18,68,35,4,57,51,20,79)=369 ;Square Sum=20049
9 Columns: Sum(37,2,75,58,50,15,25,71,36)=369 ;Square Sum=20049
2 Main diagonals: Sum(37,61,22,74,17,32,3,54,69)=369 ;Square Sum=20049
4 Broken diagonals: Sum(51,66,9,58,19,43,14,29,80)=369 ;Square Sum=20049
The form of Sudogu:
1 9 5 8 4 3 6 2 7
2 7 6 9 5 1 4 3 8
3 8 4 7 6 2 5 1 9
4 3 8 2 7 6 9 5 1
5 1 9 3 8 4 7 6 2
6 2 7 1 9 5 8 4 3
7 6 2 5 1 9 3 8 4
8 4 3 6 2 7 1 9 5
9 5 1 4 3 8 2 7 6
Row meets the rule.
Column meets the rule too.
2 main diagonals (1,9) and 4 broken diagonals (3,4,6,7) also meet the rule.
9- 3x3 Block meets the rule.
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mars15
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| Posted: Wed Jan 18, 2006 5:31 pm Post subject: Block Sum goes to magic |
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I almost forget the most important property of the 9x9 bimagic square:
9 3x3 blocks: Sum(37,18,68,2,61,33,75,53,22)=369 ;Square Sum=20049 |
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Guest
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| Posted: Sun Feb 05, 2006 4:55 pm Post subject: Re: Sudoku and magic square |
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| mars15 wrote: |
Another 9x9 panmagic square's example completely meets the rule of Sudoku showing as follow:
37 47 79 60 67 12 26 9 32 369
3 35 45 50 73 56 70 15 22 369
11 25 6 31 39 53 81 59 64 369
62 72 14 19 2 34 42 49 75 369
52 78 58 66 17 27 5 28 38 369
36 41 46 74 61 69 13 21 8 369
24 4 30 44 54 77 55 65 16 369
68 10 20 7 33 40 48 80 63 369
76 57 71 18 23 1 29 43 51 369
9 Rows: Sum(37,47,79,60,67,12,26,9,32)=369
9 Columns:Sum(37,3,11,62,52,36,24,68,76)=369
2 Main diagonals:Sum(37,35,6,19,17,69,55,80,51)=369
16 Broken diagonals:Sum(62,25,45,60,23,40,55,21,3=369
The form of Sudogu:
1 2 7 6 4 3 8 9 5 Row meets the rule.
3 8 9 5 1 2 7 6 4
2 7 6 4 3 8 9 5 1
8 9 5 1 2 7 6 4 3
7 6 4 3 8 9 5 1 2
9 5 1 2 7 6 4 3 8
6 4 3 8 9 5 1 2 7
5 1 2 7 6 4 3 8 9
4 3 8 9 5 1 2 7 6
Column meets the rule too. Some diagonals (///) also meet the rule.
9- 3x3 Block meets the rule.
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