# A (trigonometric ?) cryptography riddle

Tan: Why did $sin$ eat a sandwich?

Cot: Just $cos$!

After seeing this small "joke" made by Tan and Cot, Sin replied:

"Well, I have something better than jokes: riddles! Can you solve this one?"

tzexwx xzy mjb wn ol agl dluDa dphxyZgrgy ti

Tan then said "That seems like a terrible riddle. I'll still solve it though."

Shortly after 7 minutes of thinking, Cot said "Can you at least give us a hint?"

Sin replied:

Think this: A fruit left to ___ for almost 2 weeks (but 1 day less) and reversed; French and German; K3, but not K1 and K2 (and certainly not K4). Look for the significant, emphasized word that is the least related to the "others".

Can you help Tan and Cot out?

• Ok, so I'm not great at this sort of puzzle, and don't know much about cryptography, but some ideas that might help someone else to solve. Stop reading now if you don't want to be either hinted or misled (I don't know which) by my ramblings. 1. There appear to be 9 words in the cyphertext, so it could be a sohcahtoa mnemonic. 2. '13' reversed is 31, or 2^5-1, which may hint at base-32 encoding. 3. A fruit may be left to rot - short for rotate, and 13 minutes is an angle. Not much I know, but may help someone :) – jhabbott Jun 20 '16 at 12:26
• Pretty sure you're right about the fruit but that the 13 combines with it to make ROT13. – Gareth McCaughan Jun 20 '16 at 12:57
• Er, sorry, to be clearer, the 13 that combines with it is the "two weeks but one day less". The 13 in the question may have some other significance. – Gareth McCaughan Jun 20 '16 at 12:58
• The message is a "comeback" or response to the starting joke – HAL 9000 Jun 20 '16 at 21:08
• @jhabbot Actually, besides the trig ratio names and the starting joke, there is no relation to trignometry afterwards. You're close for the decryption methods though :) – HAL 9000 Jun 21 '16 at 19:31

Based on Sin's hints, I would think this would the meaning behind each part:

• A fruit left to ___ for almost 2 weeks (but 1 day less) = ROT13

• Reversed = Atbash, since it basically reverses the alphabet

• German = Ubchi or Enigma. These 2 make logical sense, as they were both used by the Germans in WWI and WWII. I think Ubchi makes more sense, as Sin stated in his hint to think French and German, and the French cracked Ubchi in WWI.

• French = Vigenere Cipher

• K3 = The third part of the Kryptos statue (?). It says certainly not K4, since the 4th part of the statue hasn't been cracked yet. I'm still not sure about this though.

Key for Vigenere and Ubchi =

riddles

This is largely due to the OP bolding the word others in Sin's hint. This referred to bold words as the others, and the only bold word that is also italicized is the previously mentioned word.

• German = Enigma – LeppyR64 Jun 30 '16 at 4:28
• We seem rather short of key material if there's a Vigenere and an Enigma in there... – Gareth McCaughan Jul 2 '16 at 0:51
• @icecream.sandwich You are on the right track! – HAL 9000 Sep 3 '16 at 5:34