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Loser66
 one year ago
The following is an encryption algorithm. Denote (abc) at the permutation \(a\mapsto b\), \(b\mapsto c\) and \(c\mapsto a\) and fixing all the other elements. Denote A as the following matrix
\[\left(\begin{matrix}1&4&7\\2&5&8\\3&6&9\end{matrix}\right)\]
In each step the middle row of the matrix is used to define a permutation acting on a single digit. After each step, the first column is rotated downwards and the middle column upwards, resulting a new matrix to be used for the next step of encryption
\[\left(\begin{matrix}3&5&7\\1&6&8\\2&4&9\end{matrix}\right)\]
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Loser66
 one year ago
The following is an encryption algorithm. Denote (abc) at the permutation \(a\mapsto b\), \(b\mapsto c\) and \(c\mapsto a\) and fixing all the other elements. Denote A as the following matrix \[\left(\begin{matrix}1&4&7\\2&5&8\\3&6&9\end{matrix}\right)\] In each step the middle row of the matrix is used to define a permutation acting on a single digit. After each step, the first column is rotated downwards and the middle column upwards, resulting a new matrix to be used for the next step of encryption \[\left(\begin{matrix}3&5&7\\1&6&8\\2&4&9\end{matrix}\right)\] continue on comment

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Loser66
 one year ago
Best ResponseYou've already chosen the best response.0That is , given 2,5,8, the output is 5,5,3 Question: What was the input if the output is 5,4,4,5,7,8,5 Please, help

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Please, leave guidance here. will be back . Thanks in advance.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Options A) 5,4,4,5,7,8,5 B) 8,4,8,8,7,3,8 C) 2,4,3,2,7,4,2 D) 8,4,4,5,7,1,8 E) Such input does not exists My choice E

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.2If the matrix is \[ \left(\begin{matrix}1&4&7\\2&5&8\\3&6&9\end{matrix}\right) \] and the input is 8, the output is 2 and the new matrix is \[ \left(\begin{matrix}3&5&7\\1&6&8\\2&4&9\end{matrix}\right) \] Is that correct?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Yes, My logic: From given information, if output is 5, input is 2 hence only C is a possible answer. However, after using the second matrix to find the input of 4, it must be 2, but the second digit of C is 4,that gives us C is not the correct answer > E

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0But I don't know whether it is right or wrong since I don't have the answer sheet.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0The net is on and off here. :(

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2It seems you get A back after every 3 steps

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2so it must be the case that \(5xy5mn5\) must decrypt to \(2x'y'2m'n'2\) look at the options!

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Option C is indeed correct, notice that 4 is in the last row in matrix2, so it is fixed.

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.2I spent 2 hours to brute force a solution. Mathematica is very hard to use I must say. The permutations are: \[ \begin{align*} P_1&=(2,5,8)\\ P_2&=(1,6,8)\\ P_3&=(3,4,8)\\ P_4&=(2,5,8)\\ P_5&=(1,6,8)\\ P_6&=(3,4,8)\\ P_7&=(2,5,8)\\ \end{align*} \] The inverse permutations are: \[ \begin{align*} P_1^{1}&=(8,5,2)\\ P_2^{1}&=(8,6,1)\\ P_3^{1}&=(8,4,3)\\ P_4^{1}&=(8,5,2)\\ P_5^{1}&=(8,6,1)\\ P_6^{1}&=(8,4,3)\\ P_7^{1}&=(8,5,2) \end{align*} \] Apply the inverse permutations to the output. The answer is C.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Thanks for the work. :)
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