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Quote from: Simon on November 20, 2024, 12:11:46 AMThe rule is that neighboring letters "agree" on the corners:

AKHTBN iff, for every possible pair of neighboring letters (one letter immediately following another) inside the koan, both of the following conditions hold.

• The left neighbor touches the top right corner of its own bounding box iff the right neighbor touches the top left corner of its own bounding box.
  
• The left neighbor touches the bottom right corner of its own bounding box iff the right neighbor touches the bottom left corner of its own bounding box.
  

This is exactly correct.
I wasn't very sure on picking this rule because I did not have a good way to formulate the rule in my mind at that point. Furthermore one could argue that whether a letter touches a corner or not is not exactly standardized and dependent on the font used. Decided to roll with it anyway, because as we know, if there is ambiguity about details, the master is always right (and I chose for Q not to be touching the bottom right corner).
After seeing Simon's first rule guess I kinda wish I had chosen that one because it feels very elegant.

Good guess!
Also with this post I am heading to bed so don't wait up   

White koans:
  AAA    HHH    OQ
* DO     I      QO
  E      MEL    U
  EEE    N    * VW
  END    NED    VYT
  ENE    NEE    WV
  ENN    NEN
  EXD    NNN

Black koans:
  AE      CH                 LEM
  AJ      DDD                LEMMING
* AV      DNE                NDE
* AW      EAGLE              STA
  BEGIN * EUM                STAR
  CD    * FFFFFFFXXXOZZAAA   START
  CDE     FINISH           * WM
  CED     FJ

All single letter koans are white.
E*D is white for: E H I K M N X Z (and black for every other letter)
(**), (***) and (****) is black for: B D F J L P R (and white for every other letter)

I'm totally fine with no limits if nobody just abuses it (which nobody has done so far and I don't imagine anybody here would do so).
The example you mentioned is exactly what I am afraid of, because if each round of Zendo could start with such a general broad wildcard guess, why even keep the koan guessing part and not just have the Master auto-mark every koan up to a specific length, reducing the game just to guessing the rule? Purely hypothetically of course because that's way too many koans to list and read through manually and it kind of takes away the part where people "work towards" the rule by basing guesses off of existing marked koans.
When I first read WillLem's wildcard guesses, I interpreted them as Simon's example and it made me a bit uncomfortable due to the above reason, but realizing afterwards what the guess actually looked like, it definitely has justification coming from the flow of previous guesses and koans. Not that justification is required, but it makes for a slightly better game experience if guesses are made with a goal in mind and not just with a set of RNG letters.

White koans:
  AAA    N
  E      NED
  EEE    NEE
  END    NEN
  ENE    NNN
  ENN    OQ
  EXD    QO
  HHH    U
  I      VYT
* MEL    WV

Black koans:
* AE       EAGLE
* AJ       FINISH
  BEGIN  * FJ
  CD       LEM
  CDE      LEMMING
  CED      NDE
  CH       STA
  DDD      STAR
  DNE      START

All single letter koans are white.
E*D is white for: E H I K M N X Z (and black for every other letter)
(**), (***) and (****) is black for: B D F J L P R (and white for every other letter)

Quote from: WillLem on November 19, 2024, 10:13:44 PMThe way you've done it above is fine. Example:

(*) is white for: (list of letters)

(**) is white for: (list of letters)

(***) etc.

(*) was pretty simple to mark, but everything above wasn't feasible for this particular round. Those are 676 guesses for (**) alone, and if roughly half of them are white without an easily explainable pattern, that still leaves over 300 koans to be manually marked or entered.

BUT in hindsight, reading your previous post again I realize I misunderstood what exactly you were guessing. I interpreted it as having each wildcard icon go through each letter individually, not just the same letter up to length 4. I will include those in the general patterns below the koans.

Quote from: WillLem on November 19, 2024, 10:13:44 PMFair enough, this is a good idea. One question that occurs, though: what determines a "turn"? Another user posting guesses after you? The rulemaster posting a reply to your initial guess?

Personally I think a turn should be considered the time between two rulemaster markings (once you put in a set of guesses, you can't add any more until the rulemaster has marked your last guesses). I'd also advocate for a limit of guesses per turn, but that's probably a bit harder to justify and a matter of personal taste. In the end it's just for fun though so I don't mind.

White koans:
  AAA    NED
  E      NEE
  EEE    NEN
  END    NNN
  ENE    OQ
  ENN    QO
  EXD    U
  HHH    VYT
  I      WV
  N

Black koans:
  BEGIN    FINISH
  CD       LEM
  CDE      LEMMING
  CED      NDE
  CH       STA
  DDD      STAR
  DNE      START
  EAGLE

All single letter koans are white.
E*D is white for: E H I K M N X Z (and black for every other letter)
(**), (***) and (****) is black for: B D F J L P R (and white for every other letter)

Quote from: WillLem on November 19, 2024, 06:27:10 PMEDIT: In addition, please test every letter of the alphabet individually (*), as a string of length 2 (**), as a string of length 3 (***), and as a string of length 4 (****).

Apart from the single letter koans, I don't think there is a general statement that can correctly mark all your wildcard guesses without listing them each individually, so please consider submitting only a smaller subset of guesses.
(Honestly I also feel like it's a bit of a dirty trick, since you could just submit those guesses at the beginning of every new rule without regard to the starting koans, which makes the early game kind of uninteresting and isn't usually possible in a live game of Zendo.)

White koans:
  AAA    NED
  E      NEE
  EEE    NEN
  END    NNN
  ENE  * OQ
  ENN  * QO
  EXD    U
  HHH  * VYT
  I    * WV
  N

Black koans:
  BEGIN    FINISH
  CD     * LEM
  CDE      LEMMING
  CED      NDE
  CH       STA
  DDD      STAR
  DNE      START
  EAGLE

All single letter koans are white.
E*D is white for: E H I K M N X Z

Wow, that's a really interesting guess Simon. But a counterexample is AAA which does not have matching sets as per your rule, but is marked white.

White koans:
* AAA    I
  E    * N
  EEE  * NED
  END    NEE
  ENE    NEN
  ENN    NNN
  EXD    U
  HHH

Black koans:
  BEGIN    EAGLE
  CD       FINISH
* CDE      LEMMING
  CED      NDE
  CH       STA
  DDD      STAR
  DNE      START

Quote from: Silken Healer on November 18, 2024, 08:05:57 PMNone disproved Proxmia's guess at the time of posting though, so it's still in the rules you need to provide a counter-example.

Since there's an actual turn order in live Zendo but playing by forum allows multiple guesses in one go before marking koans, I just resolved the guesses in my own particular order. We could add a "turn order" rule if you like.

Once again with the new batch of guesses there exist counterexamples to the last rule guess (and even before that the koan NDE is a counterexample).

White koans:
* E    * HHH
  EEE  * I
  END  * NEE
  ENE  * NEN
* ENN    NNN
* EXD  * U

Black koans:
  BEGIN    FINISH
* CD       LEMMING
* CED      NDE
* CH       STA
  DDD      STAR
  DNE      START
  EAGLE

Thanks! It worked like a charm.

Since one of Simon's guesses (NNN) disproves Proxima's guess of the rule, I didn't add a counterexample.

White koans:
  EEE
  END
* ENE
* NNN

Black koans:
  BEGIN
* DDD
  DNE
  EAGLE
  FINISH
  LEMMING
  NDE
* STA
  STAR
  START

I'd love to use Simon's koan formatter but I am not versed in building repos

White koans:
* EEE
  END

Black koans:
* BEGIN
* DNE
* EAGLE
* LEMMING
* FINISH
* NDE
* STAR
  START

Alright I'm going to shamelessly steal your people's table formatting because I'm pretty sure I didn't get it to work around the last time 

White koans:
* END

Black koans:
* START

Wow awesome  that is in fact a simple rule that I'm surprised hasn't been used before in a similar way.

I do have an idea but it's like 2:30am and I need to sleep but I'll think of posting it tomorrow.

I'll just shoot a wild guess: AKHTBN iff it is an English noun.

This would have been a nice entry in my "unintuitive and obscure Lix tricks waiting to be culled by Simon" level series 

Is there any list of rules that have already been played? I have an idea but I don't really want to repeat something that's similar to a rule already played. (Although one could argue that not having such a list would make it easier to play "repeat" rules, since they're more likely to be forgotten if not able to be looked up.)