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
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
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That 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, leave guidance here. will be back . Thanks in advance.
E) Such input does not exists
My choice E
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If the matrix is \[
and the input is 8, the output is 2 and the new matrix is \[
Is that correct?
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
But I don't know whether it is right or wrong since I don't have the answer sheet.
The net is on and off here. :(
It seems you get A back after every 3 steps
so it must be the case that
\(5xy5mn5\) must decrypt to \(2x'y'2m'n'2\)
look at the options!
Option C is indeed correct, notice that 4 is in the last row in matrix2, so it is fixed.
I spent 2 hours to brute force a solution. Mathematica is very hard to use I must say.
The permutations are:
The inverse permutations are:
Apply the inverse permutations to the output. The answer is C.