Reply To: Who wants to see a magic trick?

[madness]

TLW’s comment has led me down a rabbit hole, and here is what I found.
Did you know that there are 13 ciphers that are simultaneously quagmire 1 and quagmire 2 ciphers?
One is the Vigenere, which is trivially all sorts of quagmires. Another is the Beaufort, which
is created with the keyword ZYXWVUTSRQPONMLKJIHGFEDCBA. The other 11 have these “keywords”:

ADGJMPSVYBEHKNQTWZCFILORUX
AFKPUZEJOTYDINSXCHMRWBGLQV
AHOVCJQXELSZGNUBIPWDKRYFMT
AJSBKTCLUDMVENWFOXGPYHQZIR
ALWHSDOZKVGRCNYJUFQBMXITEP
APETIXMBQFUJYNCRGVKZODSHWL
ARIZQHYPGXOFWNEVMDULCTKBSJ
ATMFYRKDWPIBUNGZSLEXQJCVOH
AVQLGBWRMHCXSNIDYTOJEZUPKF
AXUROLIFCZWTQNKHEBYVSPMJGD

If you didn’t notice, then let me point out that they are the affine cipher keys.

Then today I learned that there are 13 Q3s that have all of the even-numbered rotations of the Vigenere
in their tableaux. They are created with these keywords:

ABCDEFGHIJKLMNOPQRSTUVWXYZ (trivially)
ADCFEHGJILKNMPORQTSVUXWZYB
AFCHEJGLINKPMROTQVSXUZWBYD
AHCJELGNIPKRMTOVQXSZUBWDYF
AJCLENGPIRKTMVOXQZSBUDWFYH
ALCNEPGRITKVMXOZQBSDUFWHYJ
ANCPERGTIVKXMZOBQDSFUHWJYL
APCRETGVIXKZMBODQFSHUJWLYN
ARCTEVGXIZKBMDOFQHSJULWNYP
ATCVEXGZIBKDMFOHQJSLUNWPYR
AVCXEZGBIDKFMHOJQLSNUPWRYT
AXCZEBGDIFKHMJOLQNSPURWTYV
AZCBEDGFIHKJMLONQPSRUTWVYX

Try generating a tableau and see what I mean.

And if that weren’t enough, there are (2^13)(13!)/26 (trillions) Q3 ciphers that have ROT13
as one of the lines in their tableaux. Here is an example keyword and tableau:

keyword: WVTZAQPLKRHBSJIGMNDCYXEUOF

tableau:
KGUEWZCIDNSBYXTHRJMPVQAFOL
GEAZLHWXFOCDVTRNMYUJKSBPQI
UASBGDKZLPVWRHNFOTQXMYCIJE
EZBHINLTPQWFKRMOUVAYGCDJSX
WLGIDXBPHRAZSJYTVQKOCUENMF
ZHDNXOIRJSLPGMUQAKBVEWFYCT
CWKLBIAFZTUEQPJXYOVNSMGHRD
IXZTPRFYOUDNWVKMGCESLBHQAJ
DFLPHJZOTVEXAQSYCUWMBGIRKN
NOPQRSTUVWXYZABCDEFGHIJKLM <- ROT13
SCVWALUDEXMGOFPIJNYHQRKZTB
BDWFZPENXYGIUOQJSMCRAKLTVH
YVRKSGQWAZOUPLIEXFTDJNMBHC
XTHRJMPVQAFOLKGUEWZCIDNSBY
TRNMYUJKSBPQIGEAZLHWXFOCDV
HNFOTQXMYCIJEUASBGDKZLPVWR
RMOUVAYGCDJSXEZBHINLTPQWFK
JYTVQKOCUENMFWLGIDXBPHRAZS
MUQAKBVEWFYCTZHDNXOIRJSLPG
PJXYOVNSMGHRDCWKLBIAFZTUEQ
VKMGCESLBHQAJIXZTPRFYOUDNW
QSYCUWMBGIRKNDFLPHJZOTVEXA
ABCDEFGHIJKLMNOPQRSTUVWXYZ <- identity is in every Q3 tableau
FPIJNYHQRKZTBSCVWALUDEXMGO
OQJSMCRAKLTVHBDWFZPENXYGIU
LIEXFTDJNMBHCYVRKSGQWAZOUP

Now, who will submit two lines from a tableau (but not one of my special ones) for me?
The magic trick is still on.