Zendo, play by forum

[WillLem]

So, according to the second of Simon's guesses (i.e. if the first guess turns out to be false), E and L would be non-heavy letters? (Because EEEI and LLLI have already been assigned black koans).

Just wanting to make sure I understand.

[Simon]

Right, E and L will be non-heavy. I wrote "test all 26 ..." so it's clearer what I want, even though I know some of the results already (EEEI is black).

-- Simon

[Proxima]

This is some great Zendo-science, although 51 koans is a lot to add at once. Let's see how to do this....

Here's the current list plus the first six guesses:

White koans:
CUDDLE        HISH          MLEINGM
EMMING        LEMMING       MMEMM
FFFF          LEMMINGE      MMING
FFFI          LEMMINGFISH   MMMI
FISH          LEMMINGS      MMMM
FISHING       LIMEING       MMMO
FISHLEMMING   LMMNG         PARALLELOGRAM
FLSH          MAGIC
FMSH          MIMIMIM

Black koans:
EE        GISH       LLLLLL
EEE       ING        LLLLLLL
EEEE      L          MIM
EEEI      LEM        MIN
EEING     LEMI       MINM
EI        LEMING     MM
EISH      LIME       MMI
EMM       LIMEN      MMIN
FSH       LIMENG     MMN
GGGG      LLL
GGGI      LLLI

Expectation: I expect the 4 M's to be white, the 4 F's to be white, the 4 E's to be black, and the 4 G's to be black.

All correct!

If this expectation turns out true, then I'd like to test all 26 4-letter words with all-identical characters.

Okay, I won't add these to the main list (unless you prefer me to), but:

xxxx white: B C F H J K M P Q V W X Y Z

xxxx black: A D E G I L N O R S T U

I expect FFFI to be white, GGGI to be black.

Also correct!

If this new expectation turns out true, then I'd like to test all 26 4-letter words of the form xxxI where the 3 x are all-identical characters, and the letter I is fixed at the end. (I.e., I'd like to test AAAI, BBBI, ..., ZZZI.) I'll then call a letter x heavy iff xxxI is white.

Very well!

It turns out that xxxI is white if and only if xxxx is white, i.e. the set of "heavy" letters is exactly the same as above.

But your rule guess is incorrect: LIX is white.

[Simon]

Your listing of xxxx white/black is ideal as it is. No need to expand and insert these 26 into the list of individual guesses.

Right, 51 would be a lot to add into the list. I expected at most one of the two batches (of 26 koans each) to get tested: If the xxxx batch got tested (because I was I right on 4 predictions), I wanted to fire the one guess, and then ignore the xxxI batch and its guess. Nonetheless, thanks for confirming that, for each x, the koan xxxI is marked the same as xxxx.

Now:

LLLLLLLL
X
XX
XM
XMM

-- Simon

[Proxima]

White koans:
CUDDLE        HISH          MLEINGM          XX
EMMING        LEMMING       MMEMM
FFFF          LEMMINGE      MMING
FFFI          LEMMINGFISH   MMMI
FISH          LEMMINGS      MMMM
FISHING       LIMEING       MMMO
FISHLEMMING   LMMNG         PARALLELOGRAM
FLSH          MAGIC         XM
FMSH          MIMIMIM       XMM

Black koans:
EE        GISH       LLLLLL
EEE       ING        LLLLLLL
EEEE      L          LLLLLLLL
EEEI      LEM        MIM
EEING     LEMI       MIN
EI        LEMING     MINM
EISH      LIME       MM
EMM       LIMEN      MMI
FSH       LIMENG     MMIN
GGGG      LLL        MMN
GGGI      LLLI       X

[Simon]

EXE
YY
ZZ
LLLLLLLM
LIX (known white counterexample that you can still add to the listing)

-- Simon

[Proxima]

White koans:
CUDDLE        FMSH          LMMNG        PARALLELOGRAM
EMMING        HISH          MAGIC        XM
EXE           LEMMING       MIMIMIM      XMM
FFFF          LEMMINGE      MLEINGM      XX
FFFI          LEMMINGFISH   MMEMM        ZZ
FISH          LEMMINGS      MMING
FISHING       LIMEING       MMMI
FISHLEMMING   LIX           MMMM
FLSH          LLLLLLLM      MMMO

Black koans:
EE        GISH       LLLLLL      YY
EEE       ING        LLLLLLL
EEEE      L          LLLLLLLL
EEEI      LEM        MIM
EEING     LEMI       MIN
EI        LEMING     MINM
EISH      LIME       MM
EMM       LIMEN      MMI
FSH       LIMENG     MMIN
GGGG      LLL        MMN
GGGI      LLLI       X

[Simon]

AKHTBN iff it worth 10 or more points when we play it in English Scrabble (disregarding legality according to the dictionary).

-- Simon

[Proxima]

Exactly right, well done 

[Simon]

Excellent round, thanks!

Adding more letters to a white koan keeps it white, anagramming preserves the status even when we rip apart double letters, some letters (F, H, M) reach the threshold earlier than others.

L would ostensibly never reach threshold, therefore I assumed it was worth 0, but it ended up being worth something. I would have eventually tested 20 L or 100 L. I should have known earlier; after all, MMMI was white.

I looked at the prime factorizations of the IDs of the heavy letters (B = 2 prime, C = 3 prime, D = 4 black, ...), but this was a dead end when M with ID 13 was heavy, but the super-heavy X had the highly-composite ID of 24.

Then X and Z were worth a lot and Scrabble came to mind, and when the investigation came up with the nice round threshold of 10 points (MMM costs 9, MMMI costs 10, both are known), it had to be correct. Thanks!

-- Simon

[Proxima]

Glad to know I hit around the sweet spot with difficulty. I wanted to play a harder but still solvable round after my last round from the old game (the Roman numerals one) ended in failure. The Scrabble idea was inspired by a game I'm involved with on another forum where one person thinks of a fictional character and others try to reveal the character's identity by asking questions. If a round drags on long enough, people often start to narrow it down by asking "does their name begin with a letter from A to M?" and so on; and then just for variety, in one round someone asked "Does their name start with a letter worth 1 point in Scrabble?" and that stuck in my memory

I gave a little bit of a nudge in the right direction by revealing that LIX was white, which was strictly speaking unnecessary, as I could have pointed to CUDDLE or MMIN as counterexamples.

Anyhow, your round!

[Simon]

Thanks. I don't have a good rule. I'll pass the next round to namida or WillLem, or call open floor if neither wants.

-- Simon

[namida]

Alright, sure, let's do this. (I'll check out the formatting tool later, just manual for now.)

White
POTATO

Black
CARROT

[Proxima]

CAR
POT
ROT

[WillLem]

TOMATO
BROCCOLI