The New Sudoku Players' Forum

[denis_berthier]

I think I now have a fair idea of the mostly agreed definition of an oddagon and your definition.

There is no difference between "the mostly agreed definition of an oddagon" (which you don't even mention) and mine.

I suggest you then explain in the thread "Oddagon or not Oddagon" why you consider that in SteveC's example it is not an oddagon as you told me.
As for the commonly accepted definition of the oddagon (Broken wing), I refer you to the definition of its creator RodHagglund and to the broader definition of Allan Barker among others, definitions all of which are based on the principle of guardians who are not necessarily z-candidates.

The discussion is not about broken wings, but about oddagons. In oddagons, guardians are z-candidates. I don't mind what guardians can be in other contexts (prisons, broken-wings, ...)
Allan didn't bring anything new to the definition of oddagons.

[Mauriès Robert]

The discussion is not about broken wings, but about oddagons. In oddagons, guardians are z-candidates. I don't mind what guardians can be in other contexts (prisons, broken-wings, ...)
Allan didn't bring anything new to the definition of oddagons.

So you have a personal conception of the oddagon, call it z-oddagon, it will be clearer.
Robert

[denis_berthier]

:::sigh:::

[DEFISE]

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.

Here is the same resolution as my first but instead of the 2nd oddagon [13] I found a megalodon with the same target (8r9c7) :

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
Singles: 4r6c6, 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

Resolution state:

Code: Select all

|--------------------------------------------------|
| 3    127  258  | 67   9    17   | 58   56   4    |
| 89   4    189  | 5    68   2    | 168  3    7    |
| 578  17   6    | 4    38   137  | 9    158  2    |
|--------------------------------------------------|
| 789  3    28   | 289  5    79   | 16   4    16   |
| 1    279  4    | 3    27   6    | 25   59   8    |
| 589  6    589  | 289  1    4    | 23   7    39   |
|--------------------------------------------------|
| 6    189  7    | 29   23   5    | 4    18   13   |
| 4    5    39   | 1    367  8    | 67   2    69   |
| 2    189  13   | 67   4    379  | 1378 689  5    |
|--------------------------------------------------|

oddagon[31]:
r1c4{n6 n7},c4n7{r1 r9},r9c4{n7 n6},r9n6{c4 c8},r9c8{n6 n9},c8n9{r9 r5},r5c8{n9 n5},
r5n5{c8 c7},r5c7{n5 n2},c7n2{r5 r6},r6c7{n2 n3},r6n3{c7 c9},r6c9{n3 n9},c9n9{r6 r8},
r8c9{n9 n6},c9n6{r8 r4},r4c9{n6 n1},r4n1{c9 c7},c7n1{r4 r2},r2n1{c7 c3},c3n1{r2 r9},
r9c3{n1 n3},r9n3{c3 c6},c6n3{r9 r3},r3n3{c6 c5},r3c5{n3 n8},c5n8{r3 r2},r2c5{n8 n6},
r2n6{c5 c7},b3n6{r2c7 r1c8},r1n6{c8 c4} => -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

[denis_berthier]

Here is the same resolution as my first but instead of the 2nd oddagon [13] I found a megalodon with the same target (8r9c7) :
oddagon[31]: r1c4{n6 n7},c4n7{r1 r9},r9c4{n7 n6},r9n6{c4 c8},r9c8{n6 n9},c8n9{r9 r5},r5c8{n9 n5},
r5n5{c8 c7},r5c7{n5 n2},c7n2{r5 r6},r6c7{n2 n3},r6n3{c7 c9},r6c9{n3 n9},c9n9{r6 r8},
r8c9{n9 n6},c9n6{r8 r4},r4c9{n6 n1},r4n1{c9 c7},c7n1{r4 r2},r2n1{c7 c3},c3n1{r2 r9},
r9c3{n1 n3},r9n3{c3 c6},c6n3{r9 r3},r3n3{c6 c5},r3c5{n3 n8},c5n8{r3 r2},r2c5{n8 n6},
r2n6{c5 c7},b3n6{r2c7 r1c8},r1n6{c8 c4} => -8r9c7

I'm lazy to check, but are you sure there are no loops that could be excised?

[DEFISE]

Absolutely sure. My program prevents this and I checked by hand.

[denis_berthier]

ok.

[SpAce]

The discussion is not about broken wings, but about oddagons. In oddagons, guardians are z-candidates. I don't mind what guardians can be in other contexts (prisons, broken-wings, ...) Allan didn't bring anything new to the definition of oddagons.

So you have a personal conception of the oddagon, call it z-oddagon, it will be clearer.

I must side with Robert here. I don't make any claims about knowing the history and the original definitions, and I don't have time to look into them right now, but I think I have a pretty good idea of how the term "oddagon" has been used in this section since I've been around. In that definition the guardians don't have to be z-candidates, and it's very rare that all of them are (though it's nice when it happens).

To me the most generic definition of an "oddagon" is any odd-length loop that would be impossible if all guardians were removed. It doesn't imply that the guardians must be z-candidates, which means they can be chained to the target. Thus a "z-oddagon" is a restricted special case, while most oddagons are used as krakens. To me a "Broken Wing" is an even more restricted type because it's a z-oddagon that is limited to a single digit.

This is pretty much the same position I expressed here. I don't claim at all that it's official, but it makes the most sense to me.

[denis_berthier]

To me the most generic definition of an "oddagon" is any odd-length loop that would be impossible if all guardians were removed. It doesn't imply that the guardians must be z-candidates, which means they can be chained to the target. Thus a "z-oddagon" is a restricted special case, while most oddagons are used as krakens. To me a "Broken Wing" is an even more restricted type because it's a z-oddagon that is limited to a single digit.
This is pretty much the same position I expressed here. I don't claim at all that it's official, but it makes the most sense to me.

The only problem with guardians that need only be "chained to the target" is that this doesn't define any precise pattern. They can be chained by a direct link (z-candidates) or by arbitrarily long chains. Each of the chains can be arbitrarily more complex (both in length and nature) than the oddagon itself.
This is exactly the same situation as for champagne's exocets (only J-Exocets have a real definition).
In both cases, some ad hoc reasoning must be done or some arbitrary chain(s) added before one can conclude to any elimination.
The only conclusion is: no resolution rule is defined in this view.

[DEFISE]

Hi all,
Indeed I saw that there was something unclear about these z-candidates and guardians.
For my part, I built my "oddagons" by validating the target, which means that the candidates who see it are necessarily deleted. And it's all.
Anyway I consider oddagons as gadgets because I have the impression that cases where they simplify the resolution must be very rare.

[Cenoman]

To me the most generic definition of an "oddagon" is any odd-length loop that would be impossible if all guardians were removed. It doesn't imply that the guardians must be z-candidates, which means they can be chained to the target.

I can't tell it better. Chaining guardians to a target has been my practise since SteveC made me aware of the pattern.

[SpAce]

The only problem with guardians that need only be "chained to the target" is that this doesn't define any precise pattern. They can be chained by a direct link (z-candidates) or by arbitrarily long chains. Each of the chains can be arbitrarily more complex (both in length and nature) than the oddagon itself. This is exactly the same situation as for champagne's exocets (only J-Exocets have a real definition).
In both cases, some ad hoc reasoning must be done or some arbitrary chain(s) added before one can conclude to any elimination.
The only conclusion is: no resolution rule is defined in this view.

True, but as with all deadly patterns, there's unfortunately a bit of confusion about the definitions. For example, a UR or a BUG can mean both the deadly pattern itself (without any guardians) or a specific instance with a predefined set of guardians and eliminations. If the latter is meant, I'd rather use a more specific pattern name, such as UR Type 1 or BUG+1 to avoid confusion.

For the same reason I'd prefer the plain 'Oddagon' to mean just the deadly loop (without guardians), and have specific names for certain solving patterns built around it. At the very least, I'd specify the number of guardians (e.g. Oddagon+3), though it doesn't tell whether they're being used as direct z-candidates or chained ones. That type of naming allows the player to use the generic core pattern to generate any kind of logic they wish, which is much more useful than limiting oneself to only predefined patterns.

It's the same with Exocets, which is why I think champagne's loose definition is the most useful one. Without it we'd be stuck with the strict JExocet definitions only, and things like Senior Exocets and other extensions would be hard to understand or possibly never even found. Generic definitions are better at explaining why and how a pattern actually works, and they leave room for further innovations.

[denis_berthier]

Anyway I consider oddagons as gadgets because I have the impression that cases where they simplify the resolution must be very rare.

I reached the same conclusion:

After scanning the whole collection, my initial enthusiasm for (fully super-symmetric) oddagons is shaken. I found very few interesting examples where a resolution theory is strong enough to solve the puzzle but not strong enough to destroy all the potential oddagons..

The collection mentioned here is the Obi-Wahn+Tarek collection of 563 puzzles.

In spite of their rarity (like most exotic patterns), I like oddagons for their simplicity (unless one starts to make them overly complicated by allowing any kind of extensions.