variant sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

variant sudoku

Postby steaksandwich » Mon Apr 17, 2006 1:02 pm

is anyone aware of a variant in which the player is required to place 9 completed 3x3 grids in a 9x9 grid, forming a complete sudoku puzzle?
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Postby motris » Mon Apr 17, 2006 3:46 pm

Something similar to what you are suggesting was done at the World Sudoku Championships in Lucca, Italy last month. 9 transparency slides each containing partially filled 3x3 squares were given to competitors. Those 9 pieces could then be put together in just one way to allow for a solvable sudoku grid. The combination of rotations and flips allowed from the transparency pieces (picture how 2 and 5, 6 and 9 can be rotations of each other; 1,3,4,8 can be written to allow for mirrors/rotations/both) made the puzzle somewhat interesting, but the corners were marked to simplify things a bit.

I've also seen an assembly puzzle based around a jigsaw sudoku (on a turkzeka.com competition) where the 9 regions with partially filled numbers were given and had to be cut out and reassembled to make a 9x9 square. In this variant, nothing about the numbers was needed in the assembly as the jigsaw had just one solution, so I think my first example is closer to what you are suggesting.

Giving out 9 completely filled 3x3 grids as an assembly puzzle might work alright depending on the fill, but I think the partially filled grid idea is best, to tie together some amount of manipulational logic (including different possible orientations for some of pieces by rotation/reflection) with sudoku solving as well.

Thomas Snyder
motris.livejournal.com
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Postby djape » Mon Apr 17, 2006 9:35 pm

not sure if that's what "steaksandwich" exactly had in mind, but Ruud has invented the "Clueless Sudoku" concept and he has posted a few of those puzzles on his site www.sudocue.net. I followed his idea and so far I have posted a Clueless X and a Killer Clueless on my site www.djape.net/sudoku/wp.

In those puzzles, there are 9 sudoku grids and in each one of them the center nonet has no starting clues. You can't solve any grid independently. Instead, as you start filling up center nonets, you use them together to get more clues in them because those 9 center nonets (when solved) form a valid sudoku grid, too.

Is that what you were looking for?
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Re: variant sudoku

Postby Smythe Dakota » Tue Apr 18, 2006 1:33 am

steaksandwich wrote:is anyone aware of a variant in which the player is required to place 9 completed 3x3 grids in a 9x9 grid, forming a complete sudoku puzzle?

If all the 3x3 grids are completed, and if rotations and reflections are not permitted, it would be ridiculously easy, I would think, to come up with a solution.

And the solution would never be unique. Once you have 1 solution, you can generate another just by interchanging any two of the "major" rows or columns. For example, you could interchange rows 1-2-3 with rows 4-5-6.

Since there are 6 ways to interchange major rows, and 6 ways to interchange major columns, you would then have 36 solutions on your hand, if my calculations are correct.

Bill Smythe
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Postby steaksandwich » Tue Apr 25, 2006 2:53 am

thanks to everyone.
just needed to know for a programming project.
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