In a certain code language SISTER is written as RJRUDS. How would CARPET be…

Concept

In a letter-shift (substitution) code, each letter of the original word moves a fixed number of places along the alphabet to give the coded letter. The shift can be the same for every letter, or it can follow a repeating pattern across positions. To break such a code, compare the original word with its code letter-by-letter, find the shift at each position, and then apply the very same position-wise shifts to the new word.

Decode the rule from SISTER → RJRUDS

Line up the two words and read the shift (coded letter minus original letter) at each position:

1. S → R: one step back, shift −1

2. I → J: one step forward, shift +1

3. S → R: shift −1

4. T → U: shift +1

5. E → D: shift −1

6. R → S: shift +1

So the rule is a fixed alternating pattern of shifts by position: −1, +1, −1, +1, −1, +1 — odd positions move one letter back, even positions move one letter forward.

Apply the same pattern to CARPET

1. C (pos 1, −1) → B

2. A (pos 2, +1) → B

3. R (pos 3, −1) → Q

4. P (pos 4, +1) → Q

5. E (pos 5, −1) → D

6. T (pos 6, +1) → U

Reading the coded letters in order gives BBQQDU.

Cross-check

Re-apply the derived pattern to the given example: S−1=R, I+1=J, S−1=R, T+1=U, E−1=D, R+1=S, which reproduces RJRUDS exactly. The same pattern therefore reliably turns CARPET into BBQQDU.