Cooperative Zendo

[Lambda]

t: no
ta: no
taa: yes
taaa: no
taaaa: yes
ta^5: no
ta^6: yes
ta^7: yes
ta^8: yes
ta^9: no

and since t had already been answered, I'll give you this one for free:
ta^10: yes

Koans

---

Yes:

Code: Select all

0(a^5)
0(a^6)
0(a^7)
0(a^9)
0(a^11)
0(a^12)
0(a^13)
0(a^15)
0(a^17)
0(a^18)
0(a^19)
0000 (0^4)
0000000 (0^7)
0000000000 (0^10)
002556
006525
052056
056052
056250
056502
0a (0(a^1))
0aaa (0(a^3))
506205
525600
525600minutes
52560aa
655200
7r
a0hiskey
AAA
aaa
aaaaa (a^5)
aaaaaaa (a^7)
A^7
aaaaaaaa (a^8)
A^8
aaaaaaaaa (a^9)
A^9
a^11
a^13
a^14
a^15
a^17
a^19
a^20
a^21
a^23
a^24
a^25
a^26
a^27
a^29
a^32
aig
AiR
air
aiR
aIr
aIR
Air
AIr
AIR
ari
b(a^06)
b(a^07)
b(a^08)
b(a^10)
b(a^12)
b(a^13)
b(a^14)
b(a^16)
b(a^18)
b(a^19)
b(a^20)
baa (b(a^2))
baaaa (b(a^4))
big
big^8
bigbigbig
bigbigbigbigbig
bigbigbigbigwater
bir
caa (ca^2)
caaaa (ca^4)
ca^6
ca^7
ca^8
cater
ccc
ccccc
clove
decmwaterhegamr
EaRtH
earth
earthair
f7
f7re
f7ri
fer7
fir
fir0
fir7
firewater
fiter
hot
iar
ira
jakdaws
love^16
lovelove
lovelovelovelovelove
minutes
Quickly
r7
rai
rererer
ria
stone
taa
taaaa
ta^6
ta^7
ta^8
ta^10
the
The
the^03
the^05
the^07
the^08
the^09
the^11
the^13
the^16
the^40
the^56
W
w
w(a^02) (waa)
w(a^04) (waaaa)
w(a^05)
w(a^06)
w(a^08)
w(a^10)
w(a^11)
w(a^12)
w(a^14)
w(a^16)
w(a^17)
w(a^18)
wac
WaTeR
water
water0123456789
waterbottle
whisky
witer
Wizards
www
wwwww
WWWWW
zebra

No:

Code: Select all

(empty string)
0
0(a^10)
0(a^14)
0(a^16)
0(a^20)
0(a^8)
00
000
00000 (0^5)
000000 (0^6)
00000000 (0^8)
000000000 (0^9)
0123456789
0aa (0(a^2))
0aaaa (0(a^4))
1
1o
1r
2
3
4
5
525600525600
5ire
6
6h
6ire
7
8
9
99
a
AA
aa
AAAA
aaaa
A^6
aaaaaa (a^6)
A^10
aaaaaaaaaa (a^10)
a^12
a^16
a^18
a^22
a^28
a^30
aaar
ab123456789
abcdefghijklmnopqrstuvwxyz
acir
ar
ater
b
b(a^11)
b(a^15)
b(a^17)
b(a^5)
b(a^9)
ba (b(a^1))
baaa (b(a^3))
bigbig
bigbigbigbig
Boxing
c
ca
caaa (ca^3)
ca^5
ca^9
cc
cccc
d
e
earthstone
er
f
f1re
f7r7
f8re
fe
fi
fier
fir1
fir4
fir5
fir6
fir8
fira
firc
fird
FiRe
fire
firewhisky
firf
firg
Five
fr
fr7
freshwater
g
h
hotair
i
ii
iter
j
j00ckdas
j0ckdws
jaackdaaas
jackdaws
Jump
k
l
love
lovelovelove
lovelovelovelove
m
my
n
o
of
p
q
quartz
Quikly
R
r
ri
rr
s
sphinx
t
ta
taaa
ta^5
ta^9
the^02
the^04
the^06
the^10
the^12
the^14
the^24
tr
u
v
w(a^01) (wa)
w(a^03) (waaa)
w(a^07)
w(a^09)
w(a^13)
w(a^15)
w(a^19)
waer
wate
waterzebra
watr
wr
ws
wter
ww
WW
WwWw
x
xx
xy
y
z

[DanielH]

Value 1: abct
Value 2: 0
Value 3: w, literally nothing else

I think I’d like to buy a vowel.

{ea^n | n ∈ [1,10] ∩ ℤ}

[Lambda]

ea: no
eaa: yes
eaaa: no
eaaaa: yes
ea^5: no
ea^6: yes
ea^7: yes
ea^8: yes
ea^9: no
ea^10: yes

Koans

---

Yes:

Code: Select all

0(a^5)
0(a^6)
0(a^7)
0(a^9)
0(a^11)
0(a^12)
0(a^13)
0(a^15)
0(a^17)
0(a^18)
0(a^19)
0000 (0^4)
0000000 (0^7)
0000000000 (0^10)
002556
006525
052056
056052
056250
056502
0a (0(a^1))
0aaa (0(a^3))
506205
525600
525600minutes
52560aa
655200
7r
a0hiskey
AAA
aaa
aaaaa (a^5)
aaaaaaa (a^7)
A^7
aaaaaaaa (a^8)
A^8
aaaaaaaaa (a^9)
A^9
a^11
a^13
a^14
a^15
a^17
a^19
a^20
a^21
a^23
a^24
a^25
a^26
a^27
a^29
a^32
aig
AiR
air
aiR
aIr
aIR
Air
AIr
AIR
ari
b(a^06)
b(a^07)
b(a^08)
b(a^10)
b(a^12)
b(a^13)
b(a^14)
b(a^16)
b(a^18)
b(a^19)
b(a^20)
baa (b(a^2))
baaaa (b(a^4))
big
big^8
bigbigbig
bigbigbigbigbig
bigbigbigbigwater
bir
caa (ca^2)
caaaa (ca^4)
ca^6
ca^7
ca^8
cater
ccc
ccccc
clove
decmwaterhegamr
eaa
eaaaa
ea^6
ea^7
ea^8
ea^10
EaRtH
earth
earthair
f7
f7re
f7ri
fer7
fir
fir0
fir7
firewater
fiter
hot
iar
ira
jakdaws
love^16
lovelove
lovelovelovelovelove
minutes
Quickly
r7
rai
rererer
ria
stone
taa
taaaa
ta^6
ta^7
ta^8
ta^10
the
The
the^03
the^05
the^07
the^08
the^09
the^11
the^13
the^16
the^40
the^56
W
w
w(a^02) (waa)
w(a^04) (waaaa)
w(a^05)
w(a^06)
w(a^08)
w(a^10)
w(a^11)
w(a^12)
w(a^14)
w(a^16)
w(a^17)
w(a^18)
wac
WaTeR
water
water0123456789
waterbottle
whisky
witer
Wizards
www
wwwww
WWWWW
zebra

No:

Code: Select all

(empty string)
0
0(a^10)
0(a^14)
0(a^16)
0(a^20)
0(a^8)
00
000
00000 (0^5)
000000 (0^6)
00000000 (0^8)
000000000 (0^9)
0123456789
0aa (0(a^2))
0aaaa (0(a^4))
1
1o
1r
2
3
4
5
525600525600
5ire
6
6h
6ire
7
8
9
99
a
AA
aa
AAAA
aaaa
A^6
aaaaaa (a^6)
A^10
aaaaaaaaaa (a^10)
a^12
a^16
a^18
a^22
a^28
a^30
aaar
ab123456789
abcdefghijklmnopqrstuvwxyz
acir
ar
ater
b
b(a^11)
b(a^15)
b(a^17)
b(a^5)
b(a^9)
ba (b(a^1))
baaa (b(a^3))
bigbig
bigbigbigbig
Boxing
c
ca
caaa (ca^3)
ca^5
ca^9
cc
cccc
d
e
ea
eaaa
ea^5
ea^9
earthstone
er
f
f1re
f7r7
f8re
fe
fi
fier
fir1
fir4
fir5
fir6
fir8
fira
firc
fird
FiRe
fire
firewhisky
firf
firg
Five
fr
fr7
freshwater
g
h
hotair
i
ii
iter
j
j00ckdas
j0ckdws
jaackdaaas
jackdaws
Jump
k
l
love
lovelovelove
lovelovelovelove
m
my
n
o
of
p
q
quartz
Quikly
R
r
ri
rr
s
sphinx
t
ta
taaa
ta^5
ta^9
the^02
the^04
the^06
the^10
the^12
the^14
the^24
tr
u
v
w(a^01) (wa)
w(a^03) (waaa)
w(a^07)
w(a^09)
w(a^13)
w(a^15)
w(a^19)
waer
wate
waterzebra
watr
wr
ws
wter
ww
WW
WwWw
x
xx
xy
y
z

[DanielH]

While I try to set up a program to make sure that my hypotheses so far are consistent with the existing data, I might as well have guesses open.

I notice that fir7 and fir0 are the only fir + digit guesses that are true koans. Let’s see if 0≍7 or if it might have a different value:

s/e/7/

[Lambda]

7a: yes
7aa: no
7aaa: yes
7aaaa: no
7a^5: yes
7a^6: yes
7a^7: yes
7a^8: no
7a^9: yes
7a^10: no

Koans

---

Yes:

Code: Select all

0(a^5)
0(a^6)
0(a^7)
0(a^9)
0(a^11)
0(a^12)
0(a^13)
0(a^15)
0(a^17)
0(a^18)
0(a^19)
0000 (0^4)
0000000 (0^7)
0000000000 (0^10)
002556
006525
052056
056052
056250
056502
0a (0(a^1))
0aaa (0(a^3))
506205
525600
525600minutes
52560aa
655200
7a
7aaa
7a^5
7a^6
7a^7
7a^9
7r
a0hiskey
AAA
aaa
aaaaa (a^5)
aaaaaaa (a^7)
A^7
aaaaaaaa (a^8)
A^8
aaaaaaaaa (a^9)
A^9
a^11
a^13
a^14
a^15
a^17
a^19
a^20
a^21
a^23
a^24
a^25
a^26
a^27
a^29
a^32
aig
AiR
air
aiR
aIr
aIR
Air
AIr
AIR
ari
b(a^06)
b(a^07)
b(a^08)
b(a^10)
b(a^12)
b(a^13)
b(a^14)
b(a^16)
b(a^18)
b(a^19)
b(a^20)
baa (b(a^2))
baaaa (b(a^4))
big
big^8
bigbigbig
bigbigbigbigbig
bigbigbigbigwater
bir
caa (ca^2)
caaaa (ca^4)
ca^6
ca^7
ca^8
cater
ccc
ccccc
clove
decmwaterhegamr
eaa
eaaaa
ea^6
ea^7
ea^8
ea^10
EaRtH
earth
earthair
f7
f7re
f7ri
fer7
fir
fir0
fir7
firewater
fiter
hot
iar
ira
jakdaws
love^16
lovelove
lovelovelovelovelove
minutes
Quickly
r7
rai
rererer
ria
stone
taa
taaaa
ta^6
ta^7
ta^8
ta^10
the
The
the^03
the^05
the^07
the^08
the^09
the^11
the^13
the^16
the^40
the^56
W
w
w(a^02) (waa)
w(a^04) (waaaa)
w(a^05)
w(a^06)
w(a^08)
w(a^10)
w(a^11)
w(a^12)
w(a^14)
w(a^16)
w(a^17)
w(a^18)
wac
WaTeR
water
water0123456789
waterbottle
whisky
witer
Wizards
www
wwwww
WWWWW
zebra

No:

Code: Select all

(empty string)
0
0(a^10)
0(a^14)
0(a^16)
0(a^20)
0(a^8)
00
000
00000 (0^5)
000000 (0^6)
00000000 (0^8)
000000000 (0^9)
0123456789
0aa (0(a^2))
0aaaa (0(a^4))
1
1o
1r
2
3
4
5
525600525600
5ire
6
6h
6ire
7
7aa
7aaaa
7a^8
7a^10
8
9
99
a
AA
aa
AAAA
aaaa
A^6
aaaaaa (a^6)
A^10
aaaaaaaaaa (a^10)
a^12
a^16
a^18
a^22
a^28
a^30
aaar
ab123456789
abcdefghijklmnopqrstuvwxyz
acir
ar
ater
b
b(a^11)
b(a^15)
b(a^17)
b(a^5)
b(a^9)
ba (b(a^1))
baaa (b(a^3))
bigbig
bigbigbigbig
Boxing
c
ca
caaa (ca^3)
ca^5
ca^9
cc
cccc
d
e
ea
eaaa
ea^5
ea^9
earthstone
er
f
f1re
f7r7
f8re
fe
fi
fier
fir1
fir4
fir5
fir6
fir8
fira
firc
fird
FiRe
fire
firewhisky
firf
firg
Five
fr
fr7
freshwater
g
h
hotair
i
ii
iter
j
j00ckdas
j0ckdws
jaackdaaas
jackdaws
Jump
k
l
love
lovelovelove
lovelovelovelove
m
my
n
o
of
p
q
quartz
Quikly
R
r
ri
rr
s
sphinx
t
ta
taaa
ta^5
ta^9
the^02
the^04
the^06
the^10
the^12
the^14
the^24
tr
u
v
w(a^01) (wa)
w(a^03) (waaa)
w(a^07)
w(a^09)
w(a^13)
w(a^15)
w(a^19)
waer
wate
waterzebra
watr
wr
ws
wter
ww
WW
WwWw
x
xx
xy
y
z

[DanielH]

Okay, after messing around in python, my guess for the rule is as follows:

A string is a koan if the number of characters is one less than a composite number, except 0 and 7 count double and w counts triple.

I’m fairly sure this rule works for all guesses so far. If it’s correct, where the heck did it come from‽‽

EDIT: by “fairly sure”, I mean I used Python to run the Sieve of Eratosthenes up to n = 2^20 = 1,048,576 and I verified all the things listed so far under Koans, both the yesses and nos, with the program asking me to translate anything that had an invalid character in it. I could have a bug or could have typoed an expansion of one of the exponents, but that program verified everything.

[kuuskytkolme]

Ah, it counts syllables. Ze-ro, se-ven, dou-ble u.

[Kappa]

...that's beautiful.

[DanielH]

Ah, of course! That simplifies the rule and explains why those seem to be the only ones.

[Lambda]

That's correct, congratulations!

Rule text:

Code: Select all

Pronounced aloud, one character at a time (words are spelled not read), the number of syllables is one less than a composite number. For the sake of consistency, the empty string is considered to have zero syllables; note that 1 is neither composite nor prime.

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