The New Sudoku Players' Forum

[ab]

the real test is to post a pattern that you think won't produce a puzzle in this grid.

[coloin]

There is a class of puzzles which is easy to study : the full symmetrical puzzles included in this grid.

There are exactly 16294 fully symmetrical valid puzzles, but none of them is absolutely minimal.
The number of clues varies between 28 and ... 81......

I think I understand what you have done.

your symmetrical puzzles thread
http://forum.enjoysudoku.com/viewtopic.php?t=3721&start=0

13332 patterns only !

with clues 20-37

Using this isomorph of the SF grid, you analyse all the known valid "fully symmetrical" templates.

No minimal puzzles were found in your 16294......[28-81 clues]

What would be the estimate of the number of fully symmetrical minimal puzzles of "all" the SF [or random grid] isomorphs.

isomorphs = 9! * 6^8 *2

The 9! and *2 [and some more] perhaps can be waived.....

C

[coloin]

the real test is to post a pattern that you think won't produce a puzzle in this grid.

There are patterns which wont post a pattern in any grid.

Here http://forum.enjoysudoku.com/viewtopic.php?t=5384&postdays=0&postorder=asc&start=30

Red Ed proved that this pattern

Code: Select all

x x x | x x x | x x x
x x x | . . . | x x x
x x x | . . . | x x x
------+-------+------
x . . | . . . | . . x
x . . | . x . | . . x
x . . | . . . | . . x
------+-------+------
x x x | . . . | x x x
x x x | . . . | x x x
x x x | x x x | x x x[

cant have a valid puzzle.

C

[JPF]

I think I understand what you have done.
...
Using this isomorph of the SF grid, you analyse all the known valid "fully symmetrical" templates.

I tried all the 2^15=32768 possible patterns on this SF grid. I got 32768 puzzles, but only 16294 were valid and none minimal.

JPF

[JPF]

As a by-product of the Patterns Game #42, here are 2 fully symmetric puzzles with the same pattern :

Code: Select all

 1 . 2 | . 3 . | 4 . 5
 . . . | . . . | . . .
 6 . . | 2 . 4 | . . 3
-------+-------+-------
 . . 4 | . . . | 7 . .
 2 . . | . 8 . | . . 4
 . . 1 | . . . | 5 . .
-------+-------+-------
 8 . . | 5 . 6 | . . 1
 . . . | . . . | . . .
 3 . 5 | . 4 . | 9 . 8       ER=7.2



Code: Select all

 1 . 2 | . 3 . | 4 . 5
 . . . | . . . | . . .
 3 . . | 6 . 7 | . . 8
-------+-------+-------
 . . 1 | . . . | 8 . .
 7 . . | . 2 . | . . 6
 . . 4 | . . . | 9 . .
-------+-------+-------
 6 . . | 8 . 1 | . . 3
 . . . | . . . | . . .
 4 . 8 | . 9 . | 7 . 2       ER=2.6



These 2 puzzles are not equivalent.
Their grid-solutions are isomorphic.

JPF

[Pat]

take a solved grid
and see how many different-rated puzzles can be made from it

i see a similar idea was posted by Mauricio (2006.Dec.6)

[ab]

i see a similar idea was posted by Mauricio (2006.Dec.6)

just goes to show what a great idea it was

[daj95376]

Okay, let's try this completed grid with two constraints -- \-symmetric and without 4 as a given.

Code: Select all

 +-----------------------+
 | 3 5 9 | 1 8 2 | 4 7 6 |
 | 2 1 6 | 7 4 3 | 5 9 8 |
 | 7 4 8 | 6 9 5 | 3 1 2 |
 |-------+-------+-------|
 | 6 8 7 | 4 2 1 | 9 5 3 |
 | 4 3 2 | 5 7 9 | 6 8 1 |
 | 5 9 1 | 3 6 8 | 7 2 4 |
 |-------+-------+-------|
 | 9 7 4 | 2 1 6 | 8 3 5 |
 | 1 6 3 | 8 5 7 | 2 4 9 |
 | 8 2 5 | 9 3 4 | 1 6 7 |
 +-----------------------+


How many different-rated puzzles can you construct?

[gsf]

these are minimal, all with the exact solution
edit: but rats, as ab noted, all have 4 in the givens -- deleted

[ab]

these are minimal, all with the exact solution

and they all have 4 as a given

[gsf]

here's attempt #2 -- minimal, main diagonal symmetry, no 4 in givens
this one is stingy on pearl/diamond ratings

Code: Select all

300002006000000090000695000007000003002000681501000020000010830060057200800930000 # 1.5/1.2/1.2
300102070000003000000690000607000053002000001590000700000006035100800209000930160 # 2.0/1.2/1.2
300002000000700500000690000087001000002000601500308020070010830000007209000030060 # 2.5/1.2/1.2
350000000200003590000690000007000053002000601090000000070010030060800200000930007 # 2.6/1.2/1.2
300100076000003000000690012607000053002000000090000700000006005103800000805900100 # 2.8/1.2/1.2
300000070000703500008090012080020053002500000090000700070006000103800009005900060 # 3.2/1.2/1.2
300000070000003098008600002007000053000009600090060000000010030160800200025900000 # 3.6/1.2/1.2
300000070000003590000690002007001950002000600090300000070210030160800200005000000 # 3.8/1.2/1.2
350100000200003000000690010607000953002000000090000700000206005003800009000900160 # 4.4/1.2/1.2
359002070200003008700600010007000903000000600590008020000210000103007000020900000 # 4.5/1.2/1.2
300000000010703098008605002087001000000009000091368000000000035060000200025000107 # 5.0/1.2/1.2
300100070000003008000690010607000053002000001090008720000006005103807000020930100 # 6.6/1.2/1.2
309100070000003500700605010607000053000009600091060020070010000103807000000900000 # 7.2/1.2/1.2
300002006000700500008090010080000053002000601500000720070016005003807000800930100 # 7.2/7.2/3.4
300000000000003508000690002007001950002070000090300000070200030000800209025000067 # 7.8/1.2/1.2
300102070000703008000090012680000053002000000590000720000006800103807000025900000 # 7.9/1.2/1.2
300000000000703090008090000080020003002579080090060700000006035060050200000900107 # 8.2/1.2/1.2
300002000010700508000090010080020003002500601500000700070016800003000000020930007 # 8.3/1.2/1.2
300002076010700508000090010080001003002000001500300700070006800103000000820930000 # 8.9/1.2/1.2
309000006010700008700005010080020053000500081001000700000006000003850000820930000 # 9.1/1.2/1.2


[daj95376]

Thanks gsf

You've supplied me with a number of examples to confirm that I need to check my old puzzle generator. It only generated very easy puzzles.

[tarek]

how about this special grid

Code: Select all

394862157678154923512739846726513489841296735953478261235941678469387512187625394
 3 9 4 | 8 6 2 | 1 5 7 
 6 7 8 | 1 5 4 | 9 2 3 
 5 1 2 | 7 3 9 | 8 4 6 
-------+-------+------
 7 2 6 | 5 1 3 | 4 8 9 
 8 4 1 | 2 9 6 | 7 3 5 
 9 5 3 | 4 7 8 | 2 6 1 
-------+-------+------
 2 3 5 | 9 4 1 | 6 7 8 
 4 6 9 | 3 8 7 | 5 1 2 
 1 8 7 | 6 2 5 | 3 9 4

tarek

[daj95376]

how about this special grid

While you're waiting on results from the professionals.

Code: Select all

3....2....7..5......2.39..6.....34.9.41...7.59.34...6....94.6.......7.1...762...4


Code: Select all

3.4.6..5.....5...35..739..6..65...8.841..6.....3.7..6........7.4..3.751..87.....4
3...62....7.1..9....2.....6.2...34..8...9....9..4..26..3.9.1..8.....7.12..7...39.
3...62.....815.....1...98...2.....8.84..9...59.3..8..1..5...6.....3...12....25.94
.9...21..6.8..4.2..1..3..4....5.3.8...1.....595.4.8...2.....6.8.693...1.....2.3..
.948.....67..5....5.2..9...7..5.34.9.4...6.3...347..6....9...78....875.....6..3.4
3.....1...7..5.......7.9.4...6.13..9.4.2.6..5..347..6.2.....6....9..7......62...4
..48......7.1....35....9...72.51..8....29...5..3..8..1........8...3...12.8..25394
3.4.......7..5...35.2.3.8.6..........41..6.......782....5..1678......5...87...3.4


[tarek]

Code: Select all

.................3...73.84.....1......1...73....4.8.6..35..1..8..9..7.12.8..2.3.4
. . .|. . .|. . .
. . .|. . .|. . 3
. . .|7 3 .|8 4 .
-----+-----+-----
. . .|. 1 .|. . .
. . 1|. . .|7 3 .
. . .|4 . 8|. 6 .
-----+-----+-----
. 3 5|. . 1|. . 8
. . 9|. . 7|. 1 2
. 8 .|. 2 .|3 . 4 ED=1.7/1.2/1.2