Decoding the Coding Pattern

The problem presents a coding scenario where the word ROAR is coded as URDU. We need to determine the rule used for this transformation.

• Examine the relationship between letters in ROAR and URDU:
  • R → U
  • O → R
  • A → D
  • R → U
• Calculate the shift in alphabet positions for each pair:
  • R (18) to U (21) is a shift of +3 positions.
  • O (15) to R (18) is a shift of +3 positions.
  • A (1) to D (4) is a shift of +3 positions.
  • R (18) to U (21) is a shift of +3 positions.
• The consistent pattern identified is a forward shift of 3 letters for each letter in the original word.

Applying the Pattern to Encode URDU

Using the established +3 letter shift rule, we can now encode the word URDU:

• U (21st letter) shifted by +3 becomes the 24th letter, which is X.
• R (18th letter) shifted by +3 becomes the 21st letter, which is U.
• D (4th letter) shifted by +3 becomes the 7th letter, which is G.
• U (21st letter) shifted by +3 becomes the 24th letter, which is X.

Therefore, following the code pattern, URDU is written as XUGX.