| m_b_metcalf
| | Joined: 13 Mar 2006 | | Posts: 210 | | : | | Location: Berlin |
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 Posted: Thu Mar 16, 2006 2:01 pm Post subject: Curious: s(i,j) = s(i-1, n-j+1), i and n even |
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Has anyone else ever observed even-powered sudoku grids (16x16, 36x36 etc.) which have the curious property that
s(i,j) = s(i-1, n-j+1), i and n even
i.e., that every even row (or column) is the reverse of the previous odd row (or column)?
Here is a row example:
| Code: |
6 12 8 10 15 4 11 7 5 14 1 13 16 3 2 9
9 2 3 16 13 1 14 5 7 11 4 15 10 8 12 6
4 1 15 7 2 10 12 6 8 9 3 16 5 13 14 11
11 14 13 5 16 3 9 8 6 12 10 2 7 15 1 4
14 16 4 1 7 15 5 9 12 6 13 10 2 11 3 8
8 3 11 2 10 13 6 12 9 5 15 7 1 4 16 14
5 13 10 9 14 2 16 3 4 8 11 1 12 6 7 15
15 7 6 12 1 11 8 4 3 16 2 14 9 10 13 5
2 5 1 15 3 14 10 16 13 4 12 11 8 9 6 7
7 6 9 8 11 12 4 13 16 10 14 3 15 1 5 2
12 11 14 3 9 5 2 15 1 7 6 8 4 16 10 13
13 10 16 4 8 6 7 1 15 2 5 9 3 14 11 12
3 8 2 14 5 9 15 10 11 13 16 12 6 7 4 1
1 4 7 6 12 16 13 11 10 15 9 5 14 2 8 3
10 9 5 13 4 8 3 14 2 1 7 6 11 12 15 16
16 15 12 11 6 7 1 2 14 3 8 4 13 5 9 10
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It is quite difficult to use such grids as the basis of symmetric puzzles, as the additional row symmetry is hard to disguise and they become trivial to solve once the property is noticed. Asymmetric ones are easier to set. Here is an example:
| Code: |
12 8
9 15 16 11 6 1
10 14
9 3 12 8 6 4 5 16
1 10 12 6
5 14 16 9
9 13 3 15
16 14 4 13 8 11
5 16 14 15 12
4 7 3 1 11 2
15 7 4 11 8 12 13 3
3 1 13 2 8 5
6 12 1 5 7 10 2
13 16 15 11 14 1 3 6
8 4 3 12 10 2
5 9 7 2 16 1 15 8
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I'd be interested in any comments.
Regards,
Mike Metcalf |
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