In a certain code language, the word "RAIN" is written as "OHBQ". Using the same position-based shifting pattern, how is the word "SUMMER" written in that code language?

Introduction / Context:
Here we have a non-uniform positional coding pattern. The word "RAIN" is transformed into "OHBQ", and the shifts for each letter are not the same. Instead, the amount and direction of shift vary with the position of the letter inside the word. We must detect this pattern and then apply it to the six-letter word "SUMMER".

Given Data / Assumptions:

• "RAIN" → "OHBQ".
• We must code "SUMMER".
• Alphabet positions: A = 1, B = 2, ..., Z = 26.
• The shift pattern depends on the letter position (1st, 2nd, 3rd, 4th, etc.).

Concept / Approach:
We examine the mapping for each position in RAIN. The goal is to express the movement as a sequence of numeric shifts that can repeat or extend. Observing the first, second, third, and fourth letters reveals a symmetric pattern: −3, +7, −7, +3. We then apply this repeating pattern to the letters of SUMMER.

Step-by-Step Solution:
Step 1: Determine the shifts from RAIN → OHBQ. R(18) → O(15): −3. A(1) → H(8): +7. I(9) → B(2): −7 (since 9 − 7 = 2). N(14) → Q(17): +3. Thus the pattern of shifts by position is: position 1: −3, position 2: +7, position 3: −7, position 4: +3. Step 2: Assume this 4-step pattern repeats for longer words. For a six-letter word, the shifts are: Position 1: −3. Position 2: +7. Position 3: −7. Position 4: +3. Position 5: −3 (pattern restarts). Position 6: +7. Step 3: Apply these shifts to SUMMER. Word: S U M M E R. Positions: 1 2 3 4 5 6. S(19) at position 1: 19 − 3 = 16 → P. U(21) at position 2: 21 + 7 = 28 → 28 − 26 = 2 → B. M(13) at position 3: 13 − 7 = 6 → F. M(13) at position 4: 13 + 3 = 16 → P. E(5) at position 5: 5 − 3 = 2 → B. R(18) at position 6: 18 + 7 = 25 → Y. Step 4: Combine the coded letters. SUMMER → P B F P B Y → "PBFPBY".

Verification / Alternative check:
Re-apply the same pattern to RAIN to verify that −3, +7, −7, +3 takes RAIN back to OHBQ. This confirmation gives confidence that the pattern is consistent and intended. Then check that no arithmetic mistakes have been made when wrapping around after Z.

Why Other Options Are Wrong:
Other codes either do not follow the exact −3, +7, −7, +3, −3, +7 pattern or use incorrect wrap-around arithmetic. For example, if the second letter code is not B, it would contradict the +7 shift applied to U.

Common Pitfalls:
Students often assume a simple uniform shift and fail to notice the alternating pattern. Another frequent issue is mishandling wrap-around beyond Z, which must be corrected by subtracting 26 to stay within A–Z.

Final Answer:
Using the same position-based shifting pattern, "SUMMER" is written as PBFPBY in that code language.