## grid game

Everything about Sudoku that doesn't fit in one of the other sections
After you guys are done with the SF grid, consider studying this grid:

Code: Select all
`FAX5 grid (FNC AK X with r5c5=5)136978524547123698928564713469312857871456932352897146793645281214789365685231479`

FNC = Fers (diagonally adjacent) Non-Consecutive
AK = Anti-King (diagonally adjacent cells must not be the same)
X = 2 Diagonals

Besides the grid has the following properties:
• 10-symmetrical (all cells symmetrical across r5c5 sum to 10 e.g. r1c1+r9c9, r2c7+r8c3)
• Windoku (r234c234, r234c678, r678c234, r678c678)
• DG (Disjoint Groups e.g. r147c147, r258c258)
• DG X (r159c159, r357c357)
• Old Lace (r5c5+r37c5+r5c37+r46c46)
• Star (r5c5+r46c5+r5c46+r37c37)
• Octagon (r5c5+r19c5+r5c19+r28c28)
• Girandola (r5c5+r28c5+r5c28+r19c19)
• All 3x3 boxes on c234 & c678 (e.g. r123c234, r567c678)
• c159, c234, c678 of all rows are formed by {147}, {258} or {369}
• r123, r456, r789, r159 of c14569 all sum to 15
... plus more

(Of course, if you permute the rows/columns/symbols you'll destroy a lot of these properties.)

I just like this solution grid for it includes many properties but not very canonical (i.e. it's non-trivial to re-create on a blank sheet).

Just for reference, here is a minimal puzzle with the 3 constraints of FNC, AK, X applied:
Code: Select all
` . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . .-------+-------+------- . . . | . . . | . . . . . . | . 5 . | . . . . . . | . . . | 1 . .-------+-------+------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . .`

udosuk

Posts: 2698
Joined: 17 July 2005

udosuk wrote:After you guys are done with the SF grid, consider studying this grid:

Code: Select all
`FAX5 grid (FNC AK X with r5c5=5)136978524547123698928564713469312857871456932352897146793645281214789365685231479`

12082 fully symmetric puzzles.
No minimal.

Best rating :
Code: Select all
` 1 . . | . 7 . | . . 4 . 4 . | 1 . 3 | . 9 . . . 8 | . 6 . | 7 . .-------+-------+------- . 6 . | . 1 . | . 5 . 8 . 1 | 4 . 6 | 9 . 2 . 5 . | . 9 . | . 4 .-------+-------+------- . . 3 | . 4 . | 2 . . . 1 . | 7 . 9 | . 6 . 6 . . | . 3 . | . . 9         ER=8.3`

Minimum number of clues = 28
Example :
Code: Select all
` . 3 . | . 7 . | . 2 . 5 4 . | . . . | . 9 8 . . . | 5 . 4 | . . .-------+-------+------- . . 9 | 3 . 2 | 8 . . 8 . . | . . . | . . 2 . . 2 | 8 . 7 | 1 . .-------+-------+------- . . . | 6 . 5 | . . . 2 1 . | . . . | . 6 5 . 8 . | . 3 . | . 7 .        ER=7.2`

JPF
JPF
2017 Supporter

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

Thanks JPF, great efficiency!

I'm also interested if without symmetry what's the minimum #clues? 17? 18? I can't find any 4-cell unavoidable in there but there are quite a few 6-cell ones (much like the MC grid).
udosuk

Posts: 2698
Joined: 17 July 2005

In this grid, there is no known 17s as of to date (47793 in the Gordon's list).

Here's a 18 clues puzzle :
Code: Select all
` . . . | 9 . 8 | . 2 . 5 . 7 | . . . | 6 . . . . . | . . 4 | . . .-------+-------+------- . . 9 | . . 2 | . . . . . . | . 5 . | . . . 3 . . | . . . | 1 . 6-------+-------+------- . . . | . . . | . 8 . . . . | . . 9 | . . . 6 . 5 | . 3 . | . . .`

Here are some symmetric and absolutely minimal puzzles :

Horizontal and Vertical (type III)
Code: Select all
` . . . | 9 . 8 | . . . . . 7 | . . . | 6 . . . 2 . | 5 . 4 | . 1 .-------+-------+------- 4 . . | . 1 . | . . 7 . . 1 | 4 . 6 | 9 . . 3 . . | . 9 . | . . 6-------+-------+------- . 9 . | 6 . 5 | . 8 . . . 4 | . . . | 3 . . . . . | 2 . 1 | . . .       ER=2.3`

Diagonal and Anti-diagonal (type IV)
Code: Select all
` . 3 . | . . . | . . . 5 . 7 | 1 . 3 | . 9 . . 2 . | 5 . 4 | . . .-------+-------+------- . 6 9 | 3 . . | 8 5 . . . . | . . . | . . . . 5 2 | . . 7 | 1 4 .-------+-------+------- . . . | 6 . 5 | . 8 . . 1 . | 7 . 9 | 3 . 5 . . . | . . . | . 7 .       ER=9.2`

Full Rotational (type II)
Code: Select all
` . . . | . 7 . | . . . . . . | 1 . 3 | 6 . . . 2 8 | . . 4 | 7 . .-------+-------+------- . 6 9 | 3 . 2 | . 5 . 8 . . | . . . | . . 2 . 5 . | 8 . 7 | 1 4 .-------+-------+------- . . 3 | 6 . . | 2 8 . . . 4 | 7 . 9 | . . . . . . | . 3 . | . . .       ER=8.4`

JPF
JPF
2017 Supporter

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

Thanks a lot, JPF, or should I say merci beaucoup.
udosuk

Posts: 2698
Joined: 17 July 2005

Here's the solution grid:

Code: Select all
` +-----------------------+ | 3 5 9 | 4 2 1 | 7 8 6 | | 8 1 2 | 7 9 6 | 3 5 4 | | 7 6 4 | 5 3 8 | 2 1 9 | |-------+-------+-------| | 2 9 6 | 3 8 7 | 5 4 1 | | 4 7 8 | 1 6 5 | 9 2 3 | | 1 3 5 | 2 4 9 | 8 6 7 | |-------+-------+-------| | 9 2 1 | 8 7 4 | 6 3 5 | | 5 8 7 | 6 1 3 | 4 9 2 | | 6 4 3 | 9 5 2 | 1 7 8 | +-----------------------+`

Now, how about \-diagonal symmetry without 5 (or 8 if you prefer) as a given.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Here is a list of puzzles with 8 digits and with diagonal and anti-diagonal symmetries :

300400080002006054060030000200300040008060900030009007000070030580600400040002008
000400086002006054060030000200300040008060900030009007000070030580600400640002000
000400080002006054064030000200300040008060900030009007000070630580600400040002000
000400780002000004060530009206300000008060900000009807900074030500000400043002000
300400086002000004060530000206300000008060900000009807000074030500000400640002008
300400080002000054060530000206300000008060900000009807000074030580000400040002008
300400080002000004064530000206300000008060900000009807000074630500000400040002008
300400000002000050060538000206300500008060900005009807000874030080000400000002008
000020780002000004060530009006007000408060903000200800900074030500000400043050000
000420006002006050060038000200000540408000903035000007000870030080600400600052000
000400086002006054060030000200307040008000900030209007000070030580600400640002000
000400006002006050060038000200307540008000900035209007000870030080600400600002000
009401080000090004700500200206007001070000020100200807001004005500010000040902100
009400080010000054700030000200380000008105900000049007000070005580000090040002100
009400080010090004700038000200300500078000920005009007000870005500010090040002100
350000780800090304000000019000380000070105020000049000920000000507010002043000078
350000780810090054000000009000380000070105020000049000900000000580010092043000078
309000780010090054700000009000380000070105020000049000900000005580010090043000108
309400080010000354700000010200380000000105000000049007020000005587000090040002108
309000080010090354700000010000380000070105020000049000020000005587010090040000108
309400080010000054700030000200380000008105900000049007000070005580000090040002108
050000780810090004000008009000380500070105020005049000900800000500010092043000070
009400080010000004700038000200380500008105900005049007000870005500000090040002100
359400000810000300700000210200380000000105000000049007021000005007000092000002178
009400080010090054700000200200380000070105020000049007001000005580010090040002100
009400080010000354700000210200380000000105000000049007021000005587000090040002100
009400080010000054700030200200380000008105900000049007001070005580000090040002100
350000780800090304000000019000087000070105020000240000920000000507010002043000078
359400000810000300700000010200387000000105000000249007020000005007000092000002178
009400080010000054700030000200387000008105900000249007000070005580000090040002100
009400080010000054700030000200380000008105900000049007000070005580000090040002100
009400080010090004700038000200300500078000920005009007000870005500010090040002100
350000780800090304000000019000380000070105020000049000920000000507010002043000078
350000780810090054000000009000380000070105020000049000900000000580010092043000078
309000780010090054700000009000380000070105020000049000900000005580010090043000108
309400080010000354700000010200380000000105000000049007020000005587000090040002108
309000080010090354700000010000380000070105020000049000020000005587010090040000108
309400080010000054700030000200380000008105900000049007000070005580000090040002108
050000780810090004000008009000380500070105020005049000900800000500010092043000070
009400080010000004700038000200380500008105900005049007000870005500000090040002100
359400000810000300700000210200380000000105000000049007021000005007000092000002178
009400080010090054700000200200380000070105020000049007001000005580010090040002100
009400080010000354700000210200380000000105000000049007021000005587000090040002100
009400080010000054700030200200380000008105900000049007001070005580000090040002100
350000780800090304000000019000087000070105020000240000920000000507010002043000078
359400000810000300700000010200387000000105000000249007020000005007000092000002178
009400080010000054700030000200387000008105900000249007000070005580000090040002100
350020000800006350000500010006007040400000003030200800020004000087600002000050078
350020000800006300000500210006007040400000003030200800021004000007600002000050078
350020000800006350000500010006007040400060003030200800020004000087600002000050078
350020000800006300000500210006007040400060003030200800021004000007600002000050078
000020086002000304060008210000007500400060003005200000021800030507000400640050000
000020080002000304064008210000007500400060003005200000021800630507000400040050000
350020006800006350000500010006007040400000003030200800020004000087600002600050078
350020000800006350004500010006007040400000003030200800020004600087600002000050078
350020006800006300000500210006007040400000003030200800021004000007600002600050078
350020000800006350000500210006007040400000003030200800021004000087600002000050078
050020006800006350000500210006007040400000003030200800021004000087600002600050070
350020000800006300004500210006007040400000003030200800021004600007600002000050078
050020000800006350004500210006007040400000003030200800021004600087600002000050070
350020006800000300000500210006087000400105003000240800021004000007000002600050078
350020000800000300004500210006087000400105003000240800021004600007000002000050078

Example
Code: Select all
` 3 . . | 4 . . | . 8 . . . 2 | . . 6 | . 5 4 . 6 . | . 3 . | . . .-------+-------+------- 2 . . | 3 . . | . 4 . . . 8 | . 6 . | 9 . . . 3 . | . . 9 | . . 7-------+-------+------- . . . | . 7 . | . 3 . 5 8 . | 6 . . | 4 . . . 4 . | . . 2 | . . 8`

JPF
JPF
2017 Supporter

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

JPF wrote:Here is a list of puzzles with 8 digits and with diagonal and anti-diagonal symmetries :

Yes. And every one of them has a 5 and 8 digit in the givens.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

daj95376 wrote:Here's the solution grid:

Code: Select all
` +-----------------------+ | 3 5 9 | 4 2 1 | 7 8 6 | | 8 1 2 | 7 9 6 | 3 5 4 | | 7 6 4 | 5 3 8 | 2 1 9 | |-------+-------+-------| | 2 9 6 | 3 8 7 | 5 4 1 | | 4 7 8 | 1 6 5 | 9 2 3 | | 1 3 5 | 2 4 9 | 8 6 7 | |-------+-------+-------| | 9 2 1 | 8 7 4 | 6 3 5 | | 5 8 7 | 6 1 3 | 4 9 2 | | 6 4 3 | 9 5 2 | 1 7 8 | +-----------------------+`
Now, how about \-diagonal symmetry without 5 (or 8 if you prefer) as a given.

right, it's impossible.
There is an unavoidable set with the digits 5 - 8 and with a diagonal symmetry.
Code: Select all
` *-----------------------------------------* | 3   58  9   | 4   2   1   | 7   58  6   | | 58  1   2   | 7   9   6   | 3   58  4   | | 7   6   4   | 5   3   8   | 2   1   9   | |-------------+-------------+-------------| | 2   9   6   | 3   8   7   | 5   4   1   | | 4   7   8   | 1   6   5   | 9   2   3   | | 1   3   5   | 2   4   9   | 8   6   7   | |-------------+-------------+-------------| | 9   2   1   | 8   7   4   | 6   3   5   | | 58  58  7   | 6   1   3   | 4   9   2   | | 6   4   3   | 9   5   2   | 1   7   8   | *-----------------------------------------*`
JPF
JPF
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Posts: 3754
Joined: 06 December 2005
Location: Paris, France

JPF wrote:right, it's impossible.
There is an unavoidable set with the digits 5 - 8 and with a diagonal symmetry.

Thanks JPF __ Now I know there's a reason why my puzzle generator couldn't find a puzzle for this filled grid and these two digits.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

hmmm this got me thinking. maybe for the committed compiler you could have a cross between the pattern game and the grid game. You have a grid proposed and then a pattern and you try and find the highest rated sudoku with the given pattern within an isomorph of the given grid
ab

Posts: 451
Joined: 06 September 2005

Well, just make sure that you don't pick a grid like this one and forget to include the cells with {4,5} in the pattern.

Code: Select all
` +-----------------------+ | 6 2 8 | 1 4 9 | 5 3 7 | | 9 4 7 | 5 8 3 | 2 1 6 | | 1 3 5 | 7 6 2 | 4 8 9 | |-------+-------+-------| | 5 6 4 | 3 9 7 | 8 2 1 | | 8 9 2 | 4 5 1 | 6 7 3 | | 7 1 3 | 6 2 8 | 9 5 4 | |-------+-------+-------| | 4 5 1 | 8 7 6 | 3 9 2 | | 3 8 9 | 2 1 4 | 7 6 5 | | 2 7 6 | 9 3 5 | 1 4 8 | +-----------------------+`

For some reason, my puzzle generator loved these grids. This one is from a generation of nine grids.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

daj95376 wrote:Well, just make sure that you don't pick a grid like this one and forget to include the cells with {4,5} in the pattern.

Code: Select all
` +-----------------------+ | 6 2 8 | 1 4 9 | 5 3 7 | | 9 4 7 | 5 8 3 | 2 1 6 | | 1 3 5 | 7 6 2 | 4 8 9 | |-------+-------+-------| | 5 6 4 | 3 9 7 | 8 2 1 | | 8 9 2 | 4 5 1 | 6 7 3 | | 7 1 3 | 6 2 8 | 9 5 4 | |-------+-------+-------| | 4 5 1 | 8 7 6 | 3 9 2 | | 3 8 9 | 2 1 4 | 7 6 5 | | 2 7 6 | 9 3 5 | 1 4 8 | +-----------------------+`

There is a 6-cell unavoidable set involving {45} in this grid:
Code: Select all
`+-------------+-------------+-------------+| 6   2   8   | 1   4   9   | 5   3   7   || 9   4   7   | 5   8   3   | 2   1   6   || 1   3   5   | 7   6   2   | 4   8   9   |+-------------+-------------+-------------+| 5   6   4   | 3   9   7   | 8   2   1   || 8   9   2   | 4   5   1   | 6   7   3   || 7   1   3   | 6   2   8   | 9   45  45  |+-------------+-------------+-------------+| 4   5   1   | 8   7   6   | 3   9   2   || 3   8   9   | 2   1   45  | 7   6   45  || 2   7   6   | 9   3   45  | 1   45  8   |+-------------+-------------+-------------+`

I think there are many unavoidable experts here (I'm not one of them) who can help you on this issue.
udosuk

Posts: 2698
Joined: 17 July 2005

if you swap rows 7 and 8 and columns 5 and 6, that particular unavoidable no longer has antidiagonal symmetry.
ab

Posts: 451
Joined: 06 September 2005

Yes, but you get an other one (2 digits, 4 cells) with vertical symmetry
Code: Select all
` *-----------* |628|194|537| |947|538|216| |135|726|489| |---+---+---| |564|379|821| |892|415|673| |713|682|954| |---+---+---| |389|241|765| |451|867|392| |276|953|148| *-----------*`

Code: Select all
` *-----------------------------------------* | 6   2   8   | 1   9   4   | 5   3   7   | | 9   4   7   | 5   3   8   | 2   1   6   | | 1   3   5   | 7   2   6   | 4   8   9   | |-------------+-------------+-------------| | 5   6   4   | 39  7   39  | 8   2   1   | | 8   9   2   | 4   1   5   | 6   7   3   | | 7   1   3   | 6   8   2   | 9   5   4   | |-------------+-------------+-------------| | 3   8   9   | 2   4   1   | 7   6   5   | | 4   5   1   | 8   6   7   | 3   9   2   | | 2   7   6   | 39  5   39  | 1   4   8   | *-----------------------------------------*`

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

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