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Mathematical Association of America -- Sudoku Variation

 
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chuckfresno

Joined: 16 Jun 2005
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PostPosted: Thu Sep 08, 2005 4:17 pm    Post subject: Mathematical Association of America -- Sudoku Variation Reply with quote

Ed Pegg Jr. has a must-see article on Sudoku variations here: http://www.maa.org/editorial/mathgames/mathgames_09_05_05.html

At this point, the majority of these variations are still only available in Japanese magazines. Vegard Hanssen as begun including some of the more popular varations on his site: http://www.menneske.no/sudoku/eng/
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rallveird

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PostPosted: Thu Sep 08, 2005 8:26 pm    Post subject: Reply with quote

Lots of interesting variants there. I will look into making some of them. Any wishes?
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chuckfresno

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PostPosted: Thu Sep 08, 2005 10:32 pm    Post subject: Reply with quote

The various possibilities that require more than one of each digit in each group sound the most interesting -- most likely to require all new tactics.

-- 12345 nanpure and 1234 nanpure. I haven't seen these before, but I thought of the simpler version -- 10x10 Sudokus with the numbers digits 1-5 twice in each group, 9x9 with the digits 1-3 three times in each group.

--- 1-9 and three black cells in each row, column, and region (Kuro-masu Tsuki Nanpure = Black-cell Handling).


0 to 9 Number Place seems like a very clever idea with lot's of variations possible.

The Greater Than one in the article is much tougher that others of the same type I've solved before. Some variations have numbers as clues in between cells in place of (or in combination with) the greater than signs. The number between two cells is the absolute difference between the values in those two cells.

Many of the others are similar in that they reduce the number of candidates in a large number of empty cells and therefore reduce minimum number of givens. They may not require any really new tactics.


Another interesting idea -- puzzles that have exactly TWO solutions that are as different as possible. http://sudoku.com/forums/viewtopic.php?t=1490
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rallveird

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PostPosted: Fri Sep 09, 2005 12:21 am    Post subject: Reply with quote

I've added odd/even puzzles now in different sizes. Will start to look into the others soon. I actually have made some sumdokus (the sum variant) before, but I haven't published them yet since I'm not quite happy with the ones I make for the moment.

Creating puzzles with 2 solutions isn't that hard. I could probably make all my variants into those if I wanted. But it is actually interesting to solve? Why do you want 2 solutions?
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dukuso

Joined: 14 Jul 2005
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PostPosted: Fri Sep 09, 2005 4:09 am    Post subject: Reply with quote

how about 9 solutions ?
one for each digit in the center-cell.
Then you have 9 sudokus for the price of 1 ;-)
And to make it even harder for you, let each of
the 9 puzzles have another difficulty level,
so people can start with the 1 in the center,
solve it, replace it with a 2 etc., how far they can go.


Last edited by dukuso on Fri Sep 09, 2005 12:12 pm; edited 2 times in total
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dukuso

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PostPosted: Fri Sep 09, 2005 7:07 am    Post subject: Reply with quote

how about orthogonal sudokus ?
two sudokus A,B such that each of the 81 combinations
of entries (A(x,y),B(x,y)) occurs exactly once.
You can create it as one sudoku with 2-digit entries.


how about 3D-symmetrical sudoku ?
Each minirow and each minicolumn contains exactly one
from {1,2,3},{4,5,6},{7,8,9} each.
So, when the entry in cell x,y is viewed as the
z-coordinate of a piece in the 9*9*9 cube, then you have
81 pieces in the cube with no two in the same 1*1*9 or aligned 1*3*3 box.
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rallveird

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PostPosted: Fri Sep 09, 2005 10:37 am    Post subject: Reply with quote

The 9-solutions variant where the center cell sets the difficulty sounds like a fun project, if possible at all to make.
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Nick70

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PostPosted: Fri Sep 09, 2005 11:57 am    Post subject: Reply with quote

dukuso wrote:
how about 9 solutions ?
one for each digit in the center-cell.

That's a beautiful idea, I don't think it would be possible though...
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rallveird

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PostPosted: Sat Sep 10, 2005 4:34 pm    Post subject: Reply with quote

So far I've found puzzles where 6 of the 9 numbers could be inserted in the middle to make unique 1-solution sudokus. Still looking for all the 9 numbers.
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rallveird

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PostPosted: Sat Sep 10, 2005 9:15 pm    Post subject: Reply with quote

After thinking about the 9-solution sudoku I'm not sure it's possible. The reason is simple. The startgrid can't have any numbers in B2, B4, B5, B6 and B8. The only possible places for startnumbers are the corner-boxes. So you have a sudoku where only 4 startboxes have numbers + the middle cell.
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Moschopulus

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PostPosted: Sat Sep 10, 2005 10:43 pm    Post subject: Reply with quote

rallveird wrote:
After thinking about the 9-solution sudoku I'm not sure it's possible. The reason is simple. The startgrid can't have any numbers in B2, B4, B5, B6 and B8. The only possible places for startnumbers are the corner-boxes. So you have a sudoku where only 4 startboxes have numbers + the middle cell.


Certainly you cannot have a puzzle with clues only in the 4 corner boxes and the middle cell. Then rows 4 and 6 could be interchanged in any solution to obtain another solution.

But why can't the start grid have clues in boxes 2,4,6,8 ? Surely the starting clues can be anywhere. We just want to be able to run through all digits in the centre cell.
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dukuso

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PostPosted: Sun Sep 11, 2005 6:11 am    Post subject: Reply with quote

there can be no clues in block 5,row5 or column5.
but why can't there be clues in e.g. cell (1,4) ?
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dukuso

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PostPosted: Sun Sep 11, 2005 10:02 am    Post subject: Reply with quote

here is my best so far with 1,2,5,1,2,1,2,3,2 solutions

Code:

...6..9..
.3...26.1
2..5.37..
.24......
.........
18....32.
..2..91..
8.34....6
.59..64..
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