## grid game

Everything about Sudoku that doesn't fit in one of the other sections
the real test is to post a pattern that you think won't produce a puzzle in this grid.
ab

Posts: 451
Joined: 06 September 2005

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.

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
coloin

Posts: 1697
Joined: 05 May 2005

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
coloin

Posts: 1697
Joined: 05 May 2005

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
JPF
2017 Supporter

Posts: 3754
Joined: 06 December 2005
Location: Paris, France

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

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` 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
JPF
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Posts: 3754
Joined: 06 December 2005
Location: Paris, France

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)

Pat

Posts: 3513
Joined: 18 July 2005

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

just goes to show what a great idea it was
ab

Posts: 451
Joined: 06 September 2005

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?
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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.
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

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

and they all have 4 as a given
ab

Posts: 451
Joined: 06 September 2005

here's attempt #2 -- minimal, main diagonal symmetry, no 4 in givens
this one is stingy on pearl/diamond ratings
Code: Select all
`300002006000000090000695000007000003002000681501000020000010830060057200800930000 # 1.5/1.2/1.2300102070000003000000690000607000053002000001590000700000006035100800209000930160 # 2.0/1.2/1.2300002000000700500000690000087001000002000601500308020070010830000007209000030060 # 2.5/1.2/1.2350000000200003590000690000007000053002000601090000000070010030060800200000930007 # 2.6/1.2/1.2300100076000003000000690012607000053002000000090000700000006005103800000805900100 # 2.8/1.2/1.2300000070000703500008090012080020053002500000090000700070006000103800009005900060 # 3.2/1.2/1.2300000070000003098008600002007000053000009600090060000000010030160800200025900000 # 3.6/1.2/1.2300000070000003590000690002007001950002000600090300000070210030160800200005000000 # 3.8/1.2/1.2350100000200003000000690010607000953002000000090000700000206005003800009000900160 # 4.4/1.2/1.2359002070200003008700600010007000903000000600590008020000210000103007000020900000 # 4.5/1.2/1.2300000000010703098008605002087001000000009000091368000000000035060000200025000107 # 5.0/1.2/1.2300100070000003008000690010607000053002000001090008720000006005103807000020930100 # 6.6/1.2/1.2309100070000003500700605010607000053000009600091060020070010000103807000000900000 # 7.2/1.2/1.2300002006000700500008090010080000053002000601500000720070016005003807000800930100 # 7.2/7.2/3.4300000000000003508000690002007001950002070000090300000070200030000800209025000067 # 7.8/1.2/1.2300102070000703008000090012680000053002000000590000720000006800103807000025900000 # 7.9/1.2/1.2300000000000703090008090000080020003002579080090060700000006035060050200000900107 # 8.2/1.2/1.2300002000010700508000090010080020003002500601500000700070016800003000000020930007 # 8.3/1.2/1.2300002076010700508000090010080001003002000001500300700070006800103000000820930000 # 8.9/1.2/1.2309000006010700008700005010080020053000500081001000700000006000003850000820930000 # 9.1/1.2/1.2`
Last edited by gsf on Thu Jul 31, 2008 8:55 pm, edited 1 time in total.
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

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.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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

tarek

Posts: 2644
Joined: 05 January 2006

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.....43...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..3.43.....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..253943.4.......7..5...35.2.3.8.6..........41..6.......782....5..1678......5...87...3.4`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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`

tarek

Posts: 2644
Joined: 05 January 2006

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