Zendo, play by forum

[Proxima]

SSSSSSSSS (nine)
QQQ...QQQ (65536)
QQQ...QQQ (65537)
RST
FIRST

[namida]

HTBN:
S{9}

LTBN:
Q{65536}
Q{65537}
RST
FIRST


@Simon: Do you have some kind of script you're using to make those formatted lists?

[Proxima]

Theory: Single-letter koans with a letter other than A have the buddha-nature if and only if the length is a factor of (the letter's alphabetic position - 1).

[namida]

I think you meant "if (the letter's alphabetic position - 1) is a factor of the length", but yes, I certianly cannot think of any counter-example to that theory, even though it isn't an explicit part of the rule as such. Of course, it isn't quite a solution, since it doesn't account for koans that don't consist solely of a single letter repeated multiple times.

EDIT: No, I think your wording might be the correct one. I'm bad with technical mathematics terms. But if I'm understanding you correctly, then yes, your theory is still correct.

[Simon]

No?

Let id0 be the function on single letters that maps A to 0, B to 1, C to 2, ..., Z to 25.

Then Proxima's half-rule states: For each letter c that is not A, a koan that contains exactly n >= 3 copies of c [and nothing else, EDIT Simon after namida's reply] is buddha iff id0(c) divides n. Equivalently, that koan is budda iff there exists a natural number m with id0(c) * m = n.

The marked koans violate this, because the koan BBB is black. (Everything of the form B{n} with n >= 3 appers to be black.) Also, namida mentioned there exist two letters, such that koans consisting only of copies of that letter are always black.

Noes, I can't read properly. n divides id0(c) is the claim. That would make B and C the two letters that make only black same-letter koans.

-- Simon

[namida]

The way you've worded it sounds like it applies to any koan that contains the letter that number of times. This is true when they contain nothing else but that letter X number of times, but not always true if they contain other letters as well. This doesn't mean that such a koan will never be white, though.

[Simon]

Right. Edited.

My instinct was to avoid a weird mix of regular expressions and math, but it's probably the only concise notation. >_> Let c be a letter, n >= 3. Then c{n}, which denotes n times the token c, is white iff n divides id0(c). This is true even for A, B, C, because no number >= 3 divides 1 or 2, and all numbers divide 0.

Having this for same-letter koans, there is obviously some magic happening at 3, and some method to mangle non-same-letter koans. The given example koans for anagram-changes-buddha were 3 letters long.

New koans:

SOMETHINGDDD
MIGHTYDDD
MIGHTYCC
ABC
BAC
AYZ
ZYA
YAZ
BCD

-- Simon

[namida]

White:
ABC
AYZ
ZYA
YAZ

Black:
SOMETHINGDDD
MIGHTYDDD
MIGHTYCC
BAC
BCD

[Ramon]

What about the empty koan, have we had that one yet? Or was it perhaps explicitly forbidden at some point?

[namida]

The general rules of the game define it as always black.

[Simon]

The general rules of the game disallow the empty koan. It's not part of the koanspace.

The reason is pragmatic: In the tabletop game, a marked empty koan looks like a stray marking stone.

Allowing the empty koan is a minor variant, and it doesn't affect the game. If you want to test the empty koan, then do it. Secret rules can be evaluated on the empty koan in the normal fashion. ("The X is Y" fails if there are no X, or if there are more than one X, or if there is exactly one X that is not Y.)

-- Simon

[namida]

If you wanted to evaluate that, then on this, the empty koan would be black.

[Proxima]

RTS
STR
BCA
MIGHTYQQQQ
MIGHTYGGGGGG

[namida]

White:
STR

Black:
RTS
BCA
MIGHTYQQQQ
MIGHTYGGGGGG


Maybe I should drop a few more hints...

Spoiler

1. Koans of a length less than 3 letters are explicitly defined as black by the rule; it's not just a side effect of the rules.
2. Anagrams will never have a different status if the first letter remains unchanged (but will not always have a different status just because the first letter is changed).
3. Except for koans of a length less than 3 letters, no black koans exist where at least half the letters are A.
4. There is no explicitly-defined special treatment of A in the rule. (There is no loophole going on here along the lines of "B, C, D, ... X, Y and Z have explicitly-defined special treatment", either.)

[Simon]

Koan list only.

White koans:
AAA(A*)   DOGSSS    GAMING  MIRE      SPAM
ABC       DUG       GGG     QQQQ      SSS
AKALAZAM  FIQQ      GITSMH  QQQQFIRE  SSSSSS
AMEN      FIRE      GNIGMA  QQQQQQQQ  STR
AYZ       FIREQQQQ  GOD     Q{16}     S{9}
CLAM      FREAK     GYMHIT  REQQ      YAZ
DDD       GAM       MEAN    RIFE      YIU
DIG       GAME      MEGA    SITE      ZYA
DOG       GAMERS    MIGHTS  SMH
DOGAAA    GAMESS    MIGHTY  SMIGHT

Black koans:
A          DOGCC      FIREQQQ      ING                 OA        SITES
AA         DOGE       FIREQUISITE  KLZM                OL        SOMETHINGDDD
BAC        DOGENIGHT  FIRER        LIX                 POOL      SPAMGOD
BBB        DOGF       FIRES        LOOP                Q         SS
BBBB       DOGI       FIREY        MEANT               QQ        SSSS
BBBBB      DOGRST     FIRST        MIGHT               QQQ       SSSSS
BBBBBB     DOGS       FREAKKK      MIGHTYCC            QQQQQ     TE
BCA        DOGSS      FREAKY       MIGHTYDDD           QQQQQQ    THMIG
BCD        DOGSSSS    FRQQQQ       MIGHTYDOGGY         Q{12}     TTT
BLACK      DOGT       GAMER        MIGHTYFREAKY        Q{65536}  TTTT
BLACKPOOL  DOGTOR     GAMERST      MIGHTYGGGGGG        Q{65537}  TTTTT
CCC        EEE        GAMES        MIGHTYMIGHTY        RK        TW
DDDD       EERIE      GAMESSS      MIGHTYMIGHTYMIGHTY  RMEGA     WHITE
DDDDD      ET         GIT          MIGHTYQQQQ          RS        Y
DDDDDD     FFF        HHH          MIGHTYS             RST       ZIX
DOGA       FIGHT      HOT          MIGHTYSSS           RTS
DOGAA      FIR        HOTLIX       NIGHT               S
DOGC       FIREQ      HPT          NS                  SERIF

(x)* is a repetition of (x) 0 or more times.
(x){n} is a repetition of (x) exactly n times.

-- Simon