Understanding the Coding Pattern

This question asks us to decipher a coding pattern based on an example and apply it to a new word. The example shows 'CAT' being coded as 'FDW'. This suggests a consistent rule is applied to each letter.

Analyzing the 'CAT' to 'FDW' Code

Let's examine the letter shifts using their positions in the English alphabet (A=1, B=2, C=3, ...):

• C is the 3rd letter. It is coded as F, which is the 6th letter. The shift is $6 - 3 = 3$.
• A is the 1st letter. It is coded as D, which is the 4th letter. The shift is $4 - 1 = 3$.
• T is the 20th letter. It is coded as W, which is the 23rd letter. The shift is $23 - 20 = 3$.

The pattern identified is that each letter is replaced by the letter 3 positions after it in the alphabet (a Caesar cipher with a shift of +3).

Applying the +3 Shift to 'DOG'

To find the code for 'DOG', we apply the same $+3$ shift rule to each letter:

• D: The letter 'D' is the 4th letter of the alphabet. Adding the shift: $4 + 3 = 7$. The 7th letter is G.
• O: The letter 'O' is the 15th letter of the alphabet. Adding the shift: $15 + 3 = 18$. The 18th letter is R.
• G: The letter 'G' is the 7th letter of the alphabet. Adding the shift: $7 + 3 = 10$. The 10th letter is J.

Combining these results, 'DOG' is coded as 'GRJ'.