grid game

Everything about Sudoku that doesn't fit in one of the other sections

Postby ab » Thu Jul 17, 2008 3:55 pm

the real test is to post a pattern that you think won't produce a puzzle in this grid.
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Postby coloin » Fri Jul 18, 2008 5:18 pm

JPF wrote: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

JPF wrote: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
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Postby coloin » Fri Jul 18, 2008 5:19 pm

ab wrote: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
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Postby JPF » Fri Jul 18, 2008 10:28 pm

coloin wrote: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
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Postby JPF » Thu Jul 24, 2008 2:08 pm

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
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Postby Pat » Sun Jul 27, 2008 7:56 am

ab wrote: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)
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Postby ab » Sun Jul 27, 2008 10:01 am

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

just goes to show what a great idea it was:)
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Postby daj95376 » Wed Jul 30, 2008 4:03 am

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?
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Postby gsf » Wed Jul 30, 2008 1:59 pm

these are minimal, all with the exact solution
edit: but rats, as ab noted, all have 4 in the givens -- deleted
Last edited by gsf on Thu Jul 31, 2008 8:07 am, edited 2 times in total.
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Postby ab » Wed Jul 30, 2008 2:41 pm

gsf wrote:these are minimal, all with the exact solution

and they all have 4 as a given:!:
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Postby gsf » Thu Jul 31, 2008 12:11 pm

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
Last edited by gsf on Thu Jul 31, 2008 8:55 pm, edited 1 time in total.
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Postby daj95376 » Thu Jul 31, 2008 1:38 pm

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.:(
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Postby tarek » Thu Aug 21, 2008 4:42 am

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
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Postby daj95376 » Thu Aug 21, 2008 2:04 pm

tarek wrote: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
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Postby tarek » Thu Aug 21, 2008 4:20 pm

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
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