Queen Sudoku

Everything about Sudoku that doesn't fit in one of the other sections
Condor, your QS=7 discovery can be applied to solve my puzzles posted in this thread (not the first one, which has 2 solutions):

http://forum.enjoysudoku.com/viewtopic.php?t=5408

Didn't know that it's related to the "canonical grid" though. Can we have a demonstration please? I thought the "canonical grid" was this one:
Code: Select all
`123456789456789123789123456231564897564897231897231564312645978978312645645978312`

... which clearly doesn't have QS=7.
udosuk

Posts: 2698
Joined: 17 July 2005

Red Ed wrote:Oops, sorry, I messed up earlier. There are actually 352 sets of nine non-attacking queens on a 9x9 grid, not 144 as originally claimed. The canonical grid has QS=7, which is uniquely the best among all grids that I've tested.

you have posted an isomorph of the MC grid [most canonical]
Code: Select all
`+---+---+---+|123|456|789||789|123|456||456|789|123|+---+---+---+|231|564|897||564|897|231||897|231|564|+---+---+---+|312|645|978||645|978|312||978|312|645|+---+---+---+`
Which is equivalent to yours.

Apparently there are 7, which if Red Ed is correct, on consideration looks to be only manifest in a particular isomorph of the grid..........but which ?

Since all the clues are equivalent in this grid, row swapping to the pattern will reveal all !
C
coloin

Posts: 1877
Joined: 05 May 2005

coloin wrote:you have posted the MC grid [most canonical]...

Thanks C, it seems both of us has posted a lesser canonical isomorph of the most canonical grid. The most canonical form of the MC grid should be:
Code: Select all
`+---+---+---+|123|456|789||456|789|123||789|123|456|+---+---+---+|231|564|897||564|897|231||897|231|564|+---+---+---+|312|645|978||645|978|312||978|312|645|+---+---+---+`

Thanks for the idea about morphing it. For example, here is an isomorph of it which has the diagonal (X) property:
Code: Select all
`+---+---+---+|123|456|789||456|789|123||789|123|456|+---+---+---+|897|231|564||231|564|897||564|897|231|+---+---+---+|645|978|312||978|312|645||312|645|978|+---+---+---+`

I hope someone can show us the QS=7 isomorph though.
udosuk

Posts: 2698
Joined: 17 July 2005

udosuk wrote:I hope someone can show us the QS=7 isomorph though.
It's this ...
Code: Select all
`123456789789123456456789123231564897564897231897231564312645978645978312978312645`
... with QS patterns:
Code: Select all
`1............2............3.....4......8......9..............7...5............6...2..............5......9...........7..4......8...........6...........3......1......3.............5....7...........8..........1.9...........4....6.............2........6.....9..............3......8..5...........2......1...........7...........4.......7...8............9.....1......5...............6.....4............2...3............8.....2......6...........4...........1......5..3...........9......7...............9....2....4...........5..........7..........6..1.............3....8......`
Red Ed

Posts: 633
Joined: 06 June 2005

Thanks Red Ed... It's a different QS you're referring. In my definition of QS each pattern is comprised of a single digit, not 9 different digits. Check out my link or Condor's link above to see what it means. Thanks again!
udosuk

Posts: 2698
Joined: 17 July 2005

Yeah, I was working on the definition used by the guy who started the thread ...
Red Ed

Posts: 633
Joined: 06 June 2005

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