In a certain letter code, SPINSTER is written as ROHMRSDQ by shifting each letter one step backward in the alphabet. Using the same pattern, how is SEMESTER written in that code?

Introduction / Context:
This question is based on a simple substitution cipher where each letter in a word is replaced by another letter at a fixed distance in the alphabet. SPINSTER is encoded as ROHMRSDQ, and we need to extend this pattern to encode SEMESTER. Identifying the exact shift applied to each letter and then repeating that shift is the key to solving this problem.

Given Data / Assumptions:
Original word: SPINSTER. Coded word: ROHMRSDQ. We must encode SEMESTER using the same rule. All letters are capital English letters A to Z.

Concept / Approach:
The straightforward approach is to convert each letter of SPINSTER into its alphabet position and compare it with the corresponding letter in ROHMRSDQ. If we see the same negative shift for every letter, the code uses a constant backward movement in the alphabet. Once this uniform backward shift is confirmed, we apply it letter by letter to SEMESTER to determine the coded form.

Step-by-Step Solution:
Step 1: Determine positions of letters in SPINSTER and ROHMRSDQ. S is 19, R is 18. P is 16, O is 15. I is 9, H is 8. N is 14, M is 13. S is 19, R is 18. T is 20, S is 19. E is 5, D is 4. R is 18, Q is 17. Step 2: Observe the shift. Each coded letter is exactly one position less than the original: 19 to 18, 16 to 15, 9 to 8, 14 to 13, 20 to 19, 5 to 4, and 18 to 17. Thus, the rule is: subtract 1 from the alphabet position of every letter. Step 3: Apply the same -1 shift to SEMESTER. S (19) minus 1 gives 18, which is R. E (5) minus 1 gives 4, which is D. M (13) minus 1 gives 12, which is L. E (5) minus 1 gives 4, which is D. S (19) minus 1 gives 18, which is R. T (20) minus 1 gives 19, which is S. E (5) minus 1 gives 4, which is D. R (18) minus 1 gives 17, which is Q. So SEMESTER becomes RDLDRSDQ.

Verification / Alternative check:
We can verify by reversing the operation. If we add 1 to each letter of RDLDRSDQ, we should get SEMESTER back. R plus 1 is S, D plus 1 is E, L plus 1 is M, D plus 1 is E, R plus 1 is S, S plus 1 is T, D plus 1 is E, and Q plus 1 is R. This confirms that the uniform -1 shift is correct and that RDLDRSDQ is the correct coded form of SEMESTER.

Why Other Options Are Wrong:
RDDLRSDQ and the other variants change letters in positions that should remain fixed under the -1 rule, for example repeating D where a different letter is required. Any string that does not come from subtracting 1 from each letter of SEMESTER fails to match the coding pattern demonstrated by SPINSTER and ROHMRSDQ.

Common Pitfalls:
A common mistake is miscounting alphabet positions or accidentally applying different shifts to different letters. Another error is to assume that vowels and consonants will follow different rules, even though the example clearly shows a uniform shift. The best strategy is to write out the positions explicitly, apply the shift systematically, and always verify by reversing the operation to see if the original word is recovered.

Final Answer:
Using the same one step backward shift, SEMESTER is written as RDLDRSDQ in the code language.