grid game

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

Postby udosuk » Wed Jul 02, 2008 6:37 am

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

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

136978524
547123698
928564713
469312857
871456932
352897146
793645281
214789365
685231479

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).:idea:

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

:D
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby JPF » Wed Jul 02, 2008 9:13 pm

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)

136978524
547123698
928564713
469312857
871456932
352897146
793645281
214789365
685231479

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


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Postby udosuk » Thu Jul 03, 2008 7:59 am

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

Postby JPF » Fri Jul 04, 2008 10:37 am

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
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Postby udosuk » Fri Jul 04, 2008 4:42 pm

Thanks a lot, JPF, or should I say merci beaucoup.:)
udosuk
 
Posts: 2698
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Postby daj95376 » Sat Jul 12, 2008 9:48 pm

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.
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Postby JPF » Sun Jul 13, 2008 12:08 am

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


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Postby daj95376 » Sun Jul 13, 2008 1:40 am

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.
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Postby JPF » Sun Jul 13, 2008 11:11 am

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   |
 *-----------------------------------------*
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Postby daj95376 » Sun Jul 13, 2008 2:28 pm

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.
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Postby ab » Tue Jul 15, 2008 5:48 pm

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:!:
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Postby daj95376 » Tue Jul 15, 2008 11:29 pm

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.
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Postby udosuk » Wed Jul 16, 2008 2:17 am

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.:idea:
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Joined: 17 July 2005

Postby ab » Wed Jul 16, 2008 7:23 am

if you swap rows 7 and 8 and columns 5 and 6, that particular unavoidable no longer has antidiagonal symmetry.
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Postby JPF » Wed Jul 16, 2008 10:10 pm

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   |
 *-----------------------------------------*

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