The New Sudoku Players' Forum

[denis_berthier]

Continuing with highly symmetric patterns.
The lozenge 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


And one of the puzzles:

Code: Select all

   +-------+-------+-------+
   ! 3 . . ! . 9 . ! . . 4 !
   ! . 4 . ! 5 . 2 ! . 3 . !
   ! . . 6 ! . . . ! 9 . . !
   +-------+-------+-------+
   ! . 3 . ! . 5 . ! . 4 . !
   ! 1 . . ! 3 . 6 ! . . 8 !
   ! . 6 . ! . 1 . ! . 7 . !
   +-------+-------+-------+
   ! . . 7 ! . . . ! 4 . . !
   ! . 5 . ! 1 . 8 ! . 2 . !
   ! 2 . . ! . 4 . ! . . 5 !
   +-------+-------+-------+

3...9...4.4.5.2.3...6...9...3..5..4.1..3.6..8.6..1..7...7...4...5.1.8.2.2...4...5
SER 8.3

The challenge here is not to solve the puzzle, but to find long oddagons.

[Edit]: added the general pattern

[Mauriès Robert]

Hi Denis,
Where can we find a precise definition of oddagon?
Robert

[denis_berthier]

Where can we find a precise definition of oddagon?

Good question. I don't know exactly were they originated. My first contact with them was here: http://forum.enjoysudoku.com/a-revival-of-broken-wings-t5225-91.html.
I found this pattern so nice that I immediately coded it in SudoRules when I met it.

[m_b_metcalf]

Dear Denis,
I don't know about oddagons but, FWIW, here's another version of your beautiful puzzle with even more symmetry, and minimal to boot.

Mike

Code: Select all

 4 . . . 9 . . . 3
 . 5 . 1 . 8 . 7 .
 . . 7 . . . 8 . .
 . 4 . . 8 . . 3 .
 9 . . 6 . 4 . . 1
 . 7 . . 2 . . 6 .
 . . 2 . . . 3 . .
 . 3 . 2 . 9 . 5 .   Symmetry of values of givens.
 7 . . . 1 . . . 6   Minimal. Hard.

[denis_berthier]

I don't know about oddagons but, FWIW, here's another version of your beautiful puzzle with even more symmetry, and minimal to boot.

Code: Select all

 4 . . . 9 . . . 3
 . 5 . 1 . 8 . 7 .
 . . 7 . . . 8 . .
 . 4 . . 8 . . 3 .
 9 . . 6 . 4 . . 1
 . 7 . . 2 . . 6 .
 . . 2 . . . 3 . .
 . 3 . 2 . 9 . 5 .   Symmetry of values of givens.
 7 . . . 1 . . . 6   Minimal. Hard.

Hi Mike,
Thanks for this beautiful puzzle with symmetry of the givens.
SER = 9.0, W = 6
I'm sure some players will find a means to use the symmetry for a shorter solution.

The underlying pattern is one that doesn't give many puzzles. Using gsf's program, I needed more than the full night to generate 500 puzzles, 19 of which have their SER between 9.0 and 9.2 (only one 9.2).
I filtered them with SudoRules (with the relevant settings) to find those with special properties. The puzzle in the original post is the one with the longest oddagons I've found among the 500 (and solvable by elementary reversible patterns).

[m_b_metcalf]

The underlying pattern is one that doesn't give many puzzles. Using gsf's program, I needed more than the full night to generate 500 puzzles, 19 of which have their SER between 9.0 and 9.2 (only one 9.2).
I filtered them with SudoRules (with the relevant settings) to find those with special properties. The puzzle in the original post is the one with the longest oddagons I've found among the 500 (and solvable by elementary reversible patterns).

FWIW, I generated a 9.3 in about half an hour!

Regards,

Mike

[denis_berthier]

The underlying pattern is one that doesn't give many puzzles. Using gsf's program, I needed more than the full night to generate 500 puzzles, 19 of which have their SER between 9.0 and 9.2 (only one 9.2).
I filtered them with SudoRules (with the relevant settings) to find those with special properties. The puzzle in the original post is the one with the longest oddagons I've found among the 500 (and solvable by elementary reversible patterns).

FWIW, I generated a 9.3 in about half an hour!

Great. Does it also have symmetry of givens?
Do you have some filters for high SER in your program that gsf doesn't have?

[m_b_metcalf]

FWIW, I generated a 9.3 in about half an hour!

Great. Does it also have symmetry of givens?
Do you have some filters for high SER in your program that gsf doesn't have?

It doesn't.

I'm just using the programs I wrote for the Patterns Game, finding seeds then their variations.

[Mauriès Robert]

Hi Denis,

Where can we find a precise definition of oddagon?

Good question. I don't know exactly were they originated. My first contact with them was here: http://forum.enjoysudoku.com/a-revival-of-broken-wings-t5225-91.html.
I found this pattern so nice that I immediately coded it in SudoRules when I met it.

If I understood well what I read and saw, an Oddagon attached to a Z target is an odd loop that can be formed if Z is considered true, that is to say :
Oddagon [Z,n]: {a1,a2}, {a2,a3}, ..., {a(2n-1),a2n} where n is odd and a2n=a1.
which leads to write:
a1->-a2->a3->-a4->....->a(2n-1)->-a1, which is a contradition to eliminate Z.
Robert

[denis_berthier]

If I understood well what I read and saw, an Oddagon attached to a Z target is an odd loop that can be formed if Z is considered true, that is to say :
Oddagon [Z,n]: {a1,a2}, {a2,a3}, ..., {a(2n-1),a2n} where n is odd and a2n=a1.
which leads to write:
a1->-a2->a3->-a4->....->a(2n-1)->-a1, which is a contradition to eliminate Z

Here is an example for this puzzle:
oddagon[5]: c2n9{r5 r7},b7n9{r7c2 r9c3},r9n9{c3 c8},c8n9{r9 r5},r5n9{c8 c2} ==> r9c3 ≠ 9

oddagon[5]: {a1 a2}, {a2 a3}, {a3 a4}, {a4 a5}, {a5 a1} => not Z
where each ai appears as a candidate for two different CSP-Variables and the z-candidates for each CSP-Variable are not written, as usual in my notation.

[Mauriès Robert]

Thank you Denis,
As you mentioned, an oddagon is neither a whip nor a braid. So I think that the example (http://forum.enjoysudoku.com/post288868.html#p288868) reported by SpAce in http://forum.enjoysudoku.com/a-revival-of-broken-wings-t5225-91.html is not an oddagon.
Robert

[denis_berthier]

As you mentioned, an oddagon is neither a whip nor a braid. So I think that the example (http://forum.enjoysudoku.com/post288868.html#p288868) reported by SpAce in http://forum.enjoysudoku.com/a-revival-of-broken-wings-t5225-91.html is not an oddagon.

I can't find the SpAce example at the places you mention.
An oddagon doesn't have much in common with whips or braids. It doesn't have t-candidates. All its CSP-Variables must be bivalue modulo the target.

[Mauriès Robert]

Hi Denis,
Here is the example to which SpAce refers.

Code: Select all

+---------------+---------------+-----------------+
|  5   1   27*  | 27*  3   9    | 8    4    6     |
| d27  9   3    |  6   8   4    | 1    5    2-7   |
|  6   4   8    |  1   5   27*  | 239  2379 237   |
+---------------+---------------+-----------------+
|  9   7   6    |  34  2   8    | 5    13   134   |
|  3   2   4    |  5   9   1    | 7    6    8     |
|  1   8   5    |  34  7   6    | 239  239  234   |
+---------------+---------------+-----------------+
|  8   5   1    |  27  4   3    | 6    27   9     |
|  4   6   27*  |  9   1   257* | 23   8   a2357# |
| c27  3   9    |  8   6  b257# | 4    127  1257  |
+---------------+---------------+-----------------+

In 7s, a 5-link oddagon(*) with two guardians(#).
(7)r8c9 == r9c6 - r9c1 = (7)r2c1 => -7 r2c9; stte

SteveC

If it's an Oddagon, I don't see how to write it like you do, and you can also write directly :
(7r2c9->7r3c6->7r7c4)->7r9c8->7r8c3 => 7b1 vide =>-7r2c9.
So it seems to me that we can associate a whip to 7r2c9 ?
Robert

[denis_berthier]

Hi Denis,
Here is the example to which SpAce refers.

Code: Select all

+---------------+---------------+-----------------+
|  5   1   27*  | 27*  3   9    | 8    4    6     |
| d27  9   3    |  6   8   4    | 1    5    2-7   |
|  6   4   8    |  1   5   27*  | 239  2379 237   |
+---------------+---------------+-----------------+
|  9   7   6    |  34  2   8    | 5    13   134   |
|  3   2   4    |  5   9   1    | 7    6    8     |
|  1   8   5    |  34  7   6    | 239  239  234   |
+---------------+---------------+-----------------+
|  8   5   1    |  27  4   3    | 6    27   9     |
|  4   6   27*  |  9   1   257* | 23   8   a2357# |
| c27  3   9    |  8   6  b257# | 4    127  1257  |
+---------------+---------------+-----------------+

In 7s, a 5-link oddagon(*) with two guardians(#).
(7)r8c9 == r9c6 - r9c1 = (7)r2c1 => -7 r2c9; stte

SteveC

If it's an Oddagon, I don't see how to write it like you do, and you can also write directly :
(7r2c9->7r3c6->7r7c4)->7r9c8->7r8c3 => 7b1 vide =>-7r2c9.
So it seems to me that we can associate a whip to 7r2c9 ?
Robert

For me, it's not an oddagon.

[DEFISE]

3...9...4.4.5.2.3...6...9...3..5..4.1..3.6..8.6..1..7...7...4...5.1.8.2.2...4...5
The challenge here is not to solve the puzzle, but to find long oddagons.

Hi Denis,
Here is a resolution with whips and 3 oddagons:

Hidden Text: Show

Singles: 4r5c3, 5r7c6, 4r8c1, 6r7c1
Alignment: 5-r5-b6 => -5r6c7
Alignment: 8-c5-b2 => -8r1c4 -8r3c4
Hidden pair: 16-r4c7-r4c9 => -2r4c7 -2r4c9 -9r4c9
whip[2]: c4n6{r1 r9}- c8n6{r9 .} => -6r1c7
whip[2]: c4n6{r9 r1}- c8n6{r1 .} => -6r9c7
whip[3]: r4n2{c3 c4}- r5c5{n2 n7}- r4c6{n7 .} => -9r4c3
whip[3]: c3n5{r6 r1}- c7n5{r1 r5}- b6n2{r5c7 .} => -2r6c3
whip[3]: b6n9{r6c9 r5c8}- c2n9{r5 r9}- r8n9{c3 .} => -9r7c9
whip[3]: r6n3{c7 c9}- c9n9{r6 r8}- r8c3{n9 .} => -3r8c7
whip[3]: r1c4{n7 n6}- c8n6{r1 r9}- r8c7{n6 .} => -7r1c7
whip[2]: r1n7{c4 c2}- r5n7{c2 .} => -7r2c5
whip[2]: r1n7{c4 c2}- r5n7{c2 .} => -7r3c5
whip[3]: r1c4{n7 n6}- c5n6{r2 r8}- c5n7{r8 .} => -7r4c4
whip[3]: c2n9{r7 r5}- c8n9{r5 r7}- r8n9{c9 .} => -9r9c3
whip[4]: r4c6{n9 n7}- r5c5{n7 n2}- r7c5{n2 n3}- r9c6{n3 .} => -9r6c6
Single: 4r6c6
Single: 4r3c4
Hidden pair: 67-r1c4-r9c4 => -9r9c4
whip[4]: r5c8{n9 n5}- r5c7{n5 n2}- c5n2{r5 r7}- r7c4{n2 .} => -9r7c8
whip[4]: r7c9{n3 n1}- r7c8{n1 n8}- r7c2{n8 n9}- r8c3{n9 .} => -3r8c9
whip[4]: c9n2{r3 r6}- r5n2{c7 c5}- r7c5{n2 n3}- c9n3{r7 .} => -2r3c2
Single: 2r3c9
Alignment: 7-b3-r2 => -7r2c1
whip[3]: r1n2{c2 c3}- r4c3{n2 n8}- c1n8{r4 .} => -8r1c2
whip[3]: c8n6{r1 r9}- r8c7{n6 n7}- r2n7{c7 .} => -6r2c9
whip[3]: r7c9{n1 n3}- r6c9{n3 n9}- c8n9{r5 .} => -1r9c8
Oddagon[15]: r1n6{c4 c8}- c8n6{r1 r9}- r9c8{n6 n9}- c8n9{r9 r5}- b6n9{r5c8 r6c9}- r6c9{n9 n3}- r6n3{c9 c7}- c7n3{r6 r9}- r9n3{c7 c6}- c6n3{r9 r3}- r3n3{c6 c5}- r3c5{n3 n8}- c5n8{r3 r2}- r2c5{n8 n6}- b2n6{r2c5 r1c4}- => -8r9c3
Alignment: 8-b7-c2 => -8r3c2
whip[3]: c6n1{r1 r3}- c6n3{r3 r9}- r9c3{n3 .} => -1r1c3
whip[4]: r1c6{n1 n7}- r1c4{n7 n6}- b3n6{r1c8 r2c7}- r4c7{n6 .} => -1r1c7
whip[3]: r1c7{n8 n5}- r3c8{n5 n1}- r7c8{n1 .} => -8r1c8
whip[4]: c6n1{r1 r3}- b1n1{r3c2 r2c3}- r9c3{n1 n3}- c6n3{r9 .} => -1r1c8
whip[4]: c3n1{r2 r9}- c3n3{r9 r8}- r8n9{c3 c9}- c9n7{r8 .} => -1r2c9
Single: 7r2c9
Oddagon[13]: r1n6{c4 c8}- c8n6{r1 r9}- r9c8{n6 n9}- b9n9{r9c8 r8c9}- r8n9{c9 c3}-r8c3{n9 n3}- c3n3{r8 r9}- r9c3{n3 n1}- c3n1{r9 r2}- r2n1{c3 c7}- r2c7{n1 n6}- r2n6{c7 c5}- b2n6{r2c5 r1c4}- => -8r9c7
Alignment: 8-c7-b3 => -8r3c8
whip[4]: r1n2{c2 c3}- b1n5{r1c3 r3c1}- r3c8{n5 n1}- r2n1{c7 .} => -1r1c2
Single: 1r1c6
whip[3]: r3n1{c2 c8}- r7c8{n1 n8}- r9n8{c8 .} => -1r9c2
Oddagon[15]: r1c2{n2 n7}- r1n7{c2 c4}- r1c4{n7 n6}- r1n6{c4 c8}- c8n6{r1 r9}- r9c8{n6 n8}- r9n8{c8 c2}- r9c2{n8 n9}-
r9n9{c2 c6}- c6n9{r9 r4}- r4c6{n9 n7}- r4n7{c6 c1}- b4n7{r4c1 r5c2}- r5c2{n7 n2}- c2n2{r5 r1}- => -9r5c8
STTE