When transmitting messages, a certain cipher is used. Let it be known that each of the three encrypted texts ЙМЫВОТСБЛКЪГВЦАЯЯ УКМАПОЧСРКЩВЗАХ ШМФЭОГЧСЙЪКФЬВЫЕАКК corresponded to the original message МОСКВА. Try to decrypt the three texts

ТПЕОИРВНТМОЛАРГЕИАНВИЛЕДНМТААГТДЬТКУБЧКГЕИШНЕИАЯРЯ

ЛСИЕМГОРТКРОМИТВАВКНОПКРАСЕОГНАЬЕП

РТПАИОМВСВТИЕОБПРОЕННИГЬКЕЕАМТАЛВТДЬСОУМЧШСЕОНШЬИАЯК under the condition that two of them correspond to the same message. The messages are well-known sayings. (Problem from the site www.cry.ptography.ru.)

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It can be noticed that the sequence of letters МОСКВА (MOSCVA) appears as a subsequence in each of the ciphertexts of the first trio. From this, we can understand the principle of encryption.

## Solution

It can be noticed that the sequence of letters МОСКВА (MOSCVA) appears as a subsequence in each of the ciphertexts of the first trio: йМывОтСьлКъгВцАяя (yMvOtSyKgVcAyy), укМапОчСрКщВзАх (ukMapOchSrkshVzAx), шМфэОгчСйъКфьВыеАкк (shMfeOgchSyKfyVyAk). Based on this observation, we can assume that the encryption involves inserting one or two letters into each gap between the letters of the original message (the beginning and end are also considered gaps) according to a key known only to the sender and the recipient. It is clear that the first letter of the message should appear in the 2nd or 3rd position of the encrypted text. By comparing the letters in these positions in the cryptograms to be decrypted, we conclude that the same original message corresponds to the first and third ciphertexts and that the first letter of this message is П (P). Continuing with similar reasoning, we conclude that the second letter of the repeating message is О (O) (by comparing ОИ (OI) from the 1st cryptogram and ИО (IO) from the 3rd cryptogram), and so on. In the end, we get that the first and third cryptograms correspond to the original message ПОВТОРЕНИЕМАТЬУЧЕНИЯ (POVTORENIE-MATY-UCENIYA). Now let's decrypt the second cryptogram. The first letter of the message can only be С (S) or И (I). Then, by selecting possible subsequent letters for each and eliminating obviously "unreadable" letter sequences, we get: СЕ (SE), СМ (SM), ИМ (IM), ИГ (IG) СЕГ (SEG), сео (seo), СМО (SMO), СМР (SMR), ИМО (IMO), ИМР (IMR), ИГР (IGR), игт (igt) сегр (segr), сегт (segt), СМОТ (SMOT), СМОК (SMOK), смрк (smrk), смрр (smrr), ИМОТ (IMOT), ИМОК (IMOK), имрк (imrk), имрр (imrr), игрк (igrk), игрр (igrr) СМОТР (SMOTR), СМОТО (SMOTO), СМОКО (SMOKO), смокм (smokm), ИМОТР (IMOTR), ИМОТО (IMOTO), ИМОКО (IMOKO), имокм (imokm) СМОТРМ (SMOTRM), СМОТРИ (SMOTRI), смотои (smotoi), смотот (smotot), смокои (smokoi), смокот (smokot), имотрм (imotrm), имотри (imotri), имотои (imotoi), имотот (imotot), имокои (imokoi), имокот (imokot) СМОТРИВ (SMOTRIV), СМОТРИА (SMOTRIA) СМОТРИВВ (SMOTRIVV), СМОТРИВК (SMOTRIVK), СМОТРИАК (SMOTRIAK), СМОТРИАН (SMOTRIAN) and so on. In the end, we get the original message СМОТРИВКОРЕНЬ (SMOTRIVKORENY). Answer: 1,3 - ПОВТОРЕНИЕМАТЬУЧЕНИЯ (POVTORENIE-MATY-UCENIYA), 2 - СМОТРИВКОРЕНЬ (SMOTRIVKORENY)

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