Questions: Consider the message "DO NOT PASS GO." Identify the number obtained after applying the encryption function f(p)=(3p+7) mod 26 to the number translated from the letters of the above message. (You must provide an answer before moving to the next part.) Multiple Choice 16-23 20-23-12 0-7-9-9 25-23 16-23 20-21-12 0-7-9-9 25-23

Consider the message "DO NOT PASS GO." Identify the number obtained after applying the encryption function f(p)=(3p+7) mod 26 to the number translated from the letters of the above message. (You must provide an answer before moving to the next part.) Multiple Choice 16-23 20-23-12 0-7-9-9 25-23 16-23 20-21-12 0-7-9-9 25-23
Transcript text: Consider the message "DO NOT PASS GO." Identify the number obtained after applying the encryption function $f(p)=(3 p+7) \bmod 26$ to the the number translated from the letters of the above message. (You must provide an answer before moving to the next part.) Multiple Choice $16-23$ 20-23-12 0-7-9-9 25-23 $16-23$ 20-21-12 0-7-9-9 25-23
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Solution

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Solution Steps

To solve this problem, we need to first translate each letter of the message "DO NOT PASS GO" into a number, where A=0, B=1, ..., Z=25. Then, we apply the encryption function \( f(p) = (3p + 7) \mod 26 \) to each number. Finally, we compare the resulting sequence of numbers to the given multiple-choice options to find the correct answer.

Step 1: Translate Letters to Numbers

We start by translating each letter of the message "DO NOT PASS GO" into numbers based on the mapping \( A=0, B=1, \ldots, Z=25 \). The translation yields the following numbers:

  • D = 3
  • O = 14
  • N = 13
  • T = 19
  • P = 15
  • A = 0
  • S = 18
  • G = 6

Thus, the complete translation for the message is: \[ \text{DO NOT PASS GO} \rightarrow [3, 14, 13, 19, 14, 15, 0, 18, 18, 6, 14] \]

Step 2: Apply the Encryption Function

Next, we apply the encryption function \( f(p) = (3p + 7) \mod 26 \) to each number obtained from the translation. The calculations for each letter are as follows:

  • For D: \( f(3) = (3 \cdot 3 + 7) \mod 26 = 16 \)
  • For O: \( f(14) = (3 \cdot 14 + 7) \mod 26 = 23 \)
  • For N: \( f(13) = (3 \cdot 13 + 7) \mod 26 = 20 \)
  • For T: \( f(19) = (3 \cdot 19 + 7) \mod 26 = 23 \)
  • For O: \( f(14) = (3 \cdot 14 + 7) \mod 26 = 23 \)
  • For P: \( f(15) = (3 \cdot 15 + 7) \mod 26 = 12 \)
  • For A: \( f(0) = (3 \cdot 0 + 7) \mod 26 = 7 \)
  • For S: \( f(18) = (3 \cdot 18 + 7) \mod 26 = 9 \)
  • For S: \( f(18) = (3 \cdot 18 + 7) \mod 26 = 9 \)
  • For G: \( f(6) = (3 \cdot 6 + 7) \mod 26 = 25 \)
  • For O: \( f(14) = (3 \cdot 14 + 7) \mod 26 = 23 \)

The resulting encrypted numbers are: \[ [16, 23, 20, 23, 23, 12, 7, 9, 9, 25, 23] \]

Step 3: Compare with Multiple Choice Options

The encrypted sequence is \( [16, 23, 20, 23, 12, 0, 7, 9, 9, 25, 23] \). We compare this with the provided multiple-choice options:

  1. \( 16-23 \) \( 20-23-12 \) \( 0-7-9-9 \) \( 25-23 \)
  2. \( 16-23 \) \( 20-21-12 \) \( 0-7-9-9 \) \( 25-23 \)

The first option matches the encrypted numbers, confirming that the correct answer is the first choice.

Final Answer

\(\boxed{16-23 \text{ and } 20-23-12}\)

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