Question

An encryption system operates as follows: Step 1. Fix a number $k$ ( $k \le 26$ ). Step 2. For each word, swap the first $k$ letters from the front with the last $k$ letters from the end in reverse order. If a word contains less than $2k$ letters, write the entire word in reverse order. Step 3. Replace each letter by a letter $k$ spaces ahead in the alphabet. If you cross Z in the process to move $k$ steps ahead, start again from A. Example: $k = 2$ : zebra --> arbez --> ctdgb. If the word "flight" becomes "znmorl" after encryption, then the value of k:

A.
5
B.
4
C.
7
D.
Cannot be determined uniquely from the given information
E.
6

Accepted Answer

E. "flight" has 6 letters. If $k = 6$, word length $\le 2k$, so step 2 reverses "flight" to "thgilf". Step 3 shifts each letter by 6: 't' + 6 = 'z' 'h' + 6 = 'n' 'g' + 6 = 'm' 'i' + 6 = 'o' 'l' + 6 = 'r' 'f' + 6 = 'l' Result is "znmorl". Thus, $k = 6$.

Encryption System Parameter k

Explanation

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