The New Sudoku Players' Forum

[udosuk]

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

123456789
456789123
789123456
231564897
564897231
897231564
312645978
978312645
645978312

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

[coloin]

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

[udosuk]

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.

[Red Ed]

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......

[udosuk]

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!

[Red Ed]

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