In a certain code language, the word "NIGHT" is written as "ODDGM" and the word "DARK" is written as "GOYC". Using the same pattern of letter shifts and ordering, how is the word "GREEN" written in that code language?

Introduction / Context:
This coding and decoding question uses a two step transformation on the letters of each word: first shifting letters backward through the alphabet by increasing amounts and then reversing the entire sequence. The example words "NIGHT" and "DARK" illustrate how the pattern works for words of different lengths. We must apply the same pattern to "GREEN".

Given Data / Assumptions:

• NIGHT is coded as ODDGM.
• DARK is coded as GOYC.
• We must determine the code for GREEN.
• The English alphabetical positions are used, and letter shifts are applied modularly so that going backwards from A wraps around through Z if needed.

Concept / Approach:
Consider the transformation of NIGHT. Write the letters and inspect the difference between the original and coded letters. It turns out the code is created by first shifting the letters backward by 1, 2, 3, 4 and 5 positions in order, then reversing the result. For DARK, the same idea applies with sequential backward shifts followed by reversal. For GREEN, which has five letters like NIGHT, we apply the same pattern of backward shifts 1, 2, 3, 4 and 5, then reverse the sequence to obtain the final code.

Step-by-Step Solution:
Step 1: For NIGHT, write its letters with positions: N, I, G, H, T. Step 2: Shift N back by 1 to M, I back by 2 to G, G back by 3 to D, H back by 4 to D and T back by 5 to O. This gives the intermediate sequence M G D D O. Step 3: Reverse this intermediate sequence to O D D G M, which matches ODDGM. So the rule for five letter words is confirmed. Step 4: Now apply the same backward shifts to GREEN. Step 5: Write GREEN as G, R, E, E, N. Step 6: Shift G back by 1 to F, R back by 2 to P, E back by 3 to B, E back by 4 to A and N back by 5 to I. This gives intermediate letters F, P, B, A, I. Step 7: Reverse this sequence to obtain I, A, B, P, F, which spells IABPF. Step 8: Therefore GREEN is coded as IABPF.

Verification / Alternative check:
We can test the pattern once more with DARK. D shifted back by 1 becomes C, A back by 2 becomes Y, R back by 3 becomes O and K back by 4 becomes G. The intermediate sequence is C Y O G, which when reversed becomes G O Y C, matching GOYC. This second example confirms that the method of sequential backward shifts followed by reversal is consistently used and justifies applying it to GREEN.

Why Other Options Are Wrong:
Options MCBNB, OGHVL and FPBAI involve different orderings or shift directions. They do not arise from the exact sequence of backward shifts by 1 through 5 followed by reversal. In particular, FPBAI appears as the unreversed intermediate sequence for GREEN, while the final code is the reversed form IABPF. Because the examples show that reversal is always applied, the unreversed sequence cannot be correct.

Common Pitfalls:
Many candidates correctly compute the intermediate shifted letters but forget the final reversal step, leading them to choose FPBAI. Others miscalculate one or more backward shifts, especially for letters near the beginning of the alphabet. A structured approach that carefully applies each shift and then reverses the sequence prevents these errors.

Final Answer:
Using the same shifting and reversal pattern that converts NIGHT to ODDGM, the word "GREEN" is coded as IABPF.